Nonlinear dynamics Research Papers - Academia.edu (original) (raw)

Lecture notes for UCSD PHY 221A

Actors in competitive environments are bound to decide and act under conditions of uncertainty because they rarely have accurate foreknowledge of how their opponents will respond and when they will respond. Just as a competitor makes a... more

Actors in competitive environments are bound to decide and act under conditions of uncertainty because they rarely have accurate foreknowledge of how their opponents will respond and when they will respond. Just as a competitor makes a move to improve their standing on a given variable relative to a target competitor, she should expect the latter to counteract with an iterative lagged asymmetric response, that is, with a sequence of countermoves (iteration) that is very different in kind from its trigger (asymmetry) and that will be launched at some unknown point in the future (time lag). The paper explicates the broad relevance of the newly proposed concept of " iterative lagged asymmetric responses " to the social study of temporality and to fields as diverse as intelligence and counterintelligence studies, strategic management, futures studies, military theory, and long-range planning. By bringing out in the foreground and substantiating the observation that competitive environments place a strategic premium on surprise, the concept of iterative lagged asymmetric responses makes a contribution to the never-ending and many-pronged debate about the extent to which the future can be predicted.
DOI: https://doi.org/10.1177/0961463X17752652

This paper describes the MATLAB/SIMULINK realization of the PUMA 560 robot manipulator position control methodology. This paper focuses on design, analyzed and implements nonlinear computed torque control (CTC) methods. These simulation... more

This paper describes the MATLAB/SIMULINK realization of the PUMA 560 robot manipulator
position control methodology. This paper focuses on design, analyzed and implements nonlinear
computed torque control (CTC) methods. These simulation models are developed as a part of a
software laboratory to support and enhance graduate/undergraduate robotics courses, nonlinear
control courses and MATLAB/SIMULINK courses at research and development company (SSP
Co.) research center, Shiraz, Iran.

This paper lists the Preface, Table of Contents, Index of Python Programs and the book Index.

In this study, a mathematical tunable gain model free PID-like sliding mode fuzzy controller (GTSMFC) is designed to rich the best performance. Sliding mode fuzzy controller is studied because of its model free, stable and high... more

In this study, a mathematical tunable gain model free PID-like sliding mode fuzzy controller (GTSMFC) is designed to rich the best performance. Sliding mode fuzzy controller is studied because of its model free, stable and high performance. Today, most of systems (e.g., robot manipulators) are used in unknown and unstructured environment and caused to provide sophisticated systems, therefore strong mathematical tools (e.g., nonlinear sliding mode controller) are used in artificial intelligent control methodologies to design model free nonlinear robust controller with high performance (e.g., minimum error, good trajectory, disturbance rejection). Non linear classical theories have been applied successfully in many applications, but they also have some limitation. One of the best nonlinear robust controller which can be used in uncertainty nonlinear systems, are sliding mode controller but pure sliding mode controller has some disadvantages therefore this research focuses on applied sliding mode controller in fuzzy logic theory to solve the limitation in fuzzy logic controller and sliding mode controller. One of the most important challenging in pure sliding mode controller and sliding mode fuzzy controller is sliding surface slope. This paper focuses on adjusting the gain updating factor and sliding surface slope in PID like sliding mode fuzzy controller to have the best performance and reduce the limitation.

The idea that in the near future we should expect “the Singularity” has become quite popular recently, primarily thanks to the activities of Google technical director in the field of machine training Raymond Kurzweil and his book The... more

The idea that in the near future we should expect “the Singularity” has become quite popular recently, primarily thanks to the activities of Google technical director in the field of machine training Raymond Kurzweil and his book The Singularity Is Near (2005). It is shown that the mathematical analysis of the series of events (described by Kurzweil in his famous book), which starts with the emergence of our Galaxy and ends with the decoding of the DNA code, is indeed ideally described by an extremely simple mathematical function (not known to Kurzweil himself) with a singularity in the region of 2029. It is also shown that, a similar time series (beginning with the onset of life on Earth and ending with the information revolution – composed by the Russian physicist Alexander Panov completely independently of Kurzweil) is also practically perfectly described by a mathematical function (very similar to the above and not used by Panov) with a singularity in the region of 2027. It is shown that this function is also extremely similar to the equation discovered in 1960 by Heinz von Foerster and published in his famous article in the journal “Science” – this function almost perfectly describes the dynamics of the world population and is characterized by a mathematical singularity in the region of 2027. All this indicates the existence of sufficiently rigorous global macroevolutionary regularities (describing the evolution of complexity on our planet for a few billion of years), which can be surprisingly accurately described by extremely simple mathematical functions. At the same time it is demonstrated that in the region of the singularity point there is no reason, after Kurzweil, to expect an unprecedented (many orders of magnitude) acceleration of the rates of technological development. There are more grounds for interpreting this point as an indication of an inflection point, after which the pace of global evolution will begin to slow down systematically in the long term.

Lucretius was the first philosopher of immanence. It is he and not Democritus or Epicurus who holds this title. If we want to understand the historical emergence of the concept of immanence, we should start by distinguishing its... more

Lucretius was the first philosopher of immanence. It is he and not Democritus or Epicurus who holds this title. If we want to understand the historical emergence of the concept of immanence, we should start by distinguishing its precursors in Greek atomism from its first complete incarnation in Lucretius. This way, we can see exactly what first defined and distinguished immanence from its past. Therefore in what follows I would like to make three, perhaps controversial, claims about the emergence of philosophical immanence. 1) Lucretius was not an atomist, 2) Greek atomism reintroduced transcendence, and 3) It is the primacy of motion in Lucretius that defines his philosophical immanence. Lucretius was not an atomist This thesis is as counterintuitive as it is straightforward. The first major difference between Lucretius and the earlier Greek atomists is precisely that—the atom. For Leucippus, Democritus, and Epicurus atoms are always in motion, but the atom itself remained fundamentally unchanged, indivisible, and thus internally static—even as it moved. Thus instead of positing discrete atoms as ontologically primary as both ancient Greek and later modern theories do, one of Lucretius's greatest novelties was to posit the movement or flow of matter as primary. Lucretius did not simply " translate Epicurus, " as the Greco-centric story goes; rather, he introduced the first immanent kinetic materialism in the West. For example, although the Latin word atomus (smallest particle) was available to Lucretius to use in his poem, he intentionally did not use it, nor did he use the Latin word particula or particle to describe matter. The English translations of " atom, " " particle, " and others have all been added to the text in translation based on a certain historical interpretation of it. The idea that Lucretius subscribed to a world of discrete particles called atoms is therefore both a projection of Epicureanism, who used the Greek word atomos, and a retroaction of modern scientific mechanism of the fifteenth century onto De Rerum Natura. Lucretius rejected entirely the notion that things emerged from discrete particles. To believe otherwise is to distort the original meanings of the Latin text as well as the absolutely enormous poetic apparatus he summoned to describe the flowing, swirling, folding, and weaving of the flux of matter. Although Lucretius rejected the term atomus, he remained absolutely true to one aspect of the original Greek meaning of the word, τομος (átomos, " indivisible "), from-(a-, " not ") + τέμνω (témnō, " I cut "). Being is not cut up into discrete particles, but is composed of continuous flows, folds, and weaves. Discrete " things " (rerum) are composed of corporeal flows (corpora) that move together (conflux) and fold over themselves (nexus) in a woven knot work (contextum). For Lucretius, things only emerge and have their being within and immanent to the flow and flux of matter in motion. Discreteness is an apparent product of continuous folded matter, uncut, undivided, and in motion and not the other way around.

An Aircraft Dynamics Model (ADM) augmentation scheme for Remotely Piloted Aircraft System (RPAS) navigation and guidance is presented. The proposed ADM virtual sensor is employed in the RPAS navigation system to enhance continuity and... more

An Aircraft Dynamics Model (ADM) augmentation scheme for Remotely Piloted Aircraft System (RPAS) navigation and guidance is presented. The proposed ADM virtual sensor is employed in the RPAS navigation system to enhance continuity and accuracy of positioning data in case of Global Navigation Satellite System (GNSS) data degradations/losses, and to improve attitude estimation by vision based sensors and Micro-Electromechanical System Inertial Measurement Unit (MEMS-IMU) sensors. The ADM virtual sensor is essentially a knowledge-based module that predicts RPAS flight dynamics (aircraft trajectory and attitude motion) by employing a rigid body 6-Degree of Freedom (6-DoF) model. Two possible schemes are studied for integration of the ADM module in the aircraft navigation system employing an Extended Kalman Filter (EKF) and an Unscented Kalman Filter (UKF). Additionally, the synergy between the navigation systems and an Avionics-Based Integrity Augmentation (ABIA) module is examined and a sensor-switching framework is proposed to maintain the Required Navigation Performance (RNP) in the event of single and multiple sensor degradations. The ADM performance is assessed through simulation of an RPAS in representative fight operations. Sensitivity analysis of the errors caused by perturbations in the input parameters of the aircraft dynamics is performed to demonstrate the robustness of the proposed approach. Results confirm that the ADM virtual sensor provides improved performance in terms of data accuracy/continuity, and an extension of solution validity time, especially when pre-filtered and employed in conjunction with a UKF.

SUMMARY: The structural design requirements of an offshore platform subjected wave induced forces and moments in the jacket can play a major role in the design of the offshore structures. For an economic and reliable design; good... more

SUMMARY: The structural design requirements of an offshore platform subjected wave induced forces and moments in the jacket can play a major role in the design of the offshore structures. For an economic and reliable design; good estimation of wave loadings are essential. A nonlinear response analysis of a fixed offshore platform under wave loading is presented, the structure is discretized using the finite element method, wave force is determined according to linearized Morison equation. Hydrodynamic loading on horizontal and vertical tubular members and the dynamic response of fixed offshore structure together with the distribution of displacement, axial force and bending moment along the leg are investigated for regular and extreme conditions, where the structure should keep production capability in conditions of the one year return period wave and must be able to survive the 100 year return period storm conditions. The result of the study shows that the nonlinear response investigation is quite crucial for safe design and operation of offshore platform.

Owens and Kantabutra. “Using Agent-Based Modeling (ABM) to simulate, within the context of the Intentionally-Linked Entities (ILE) database management system, missing information: To explain self-organization and emergence in world... more

Owens and Kantabutra. “Using Agent-Based Modeling (ABM) to simulate, within the context of the Intentionally-Linked Entities (ILE) database management system, missing information: To explain self-organization and emergence in world commercial and political networks during the First Global Age, 1400-1800.”
Paper for the session “Social Network Analysis and Multi-Relational Databases on Comparative Studies in China and Europe”; 18th World Economic History Congress, Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts, USA, July 29-August 3, 2018 [Tues., 31 July, Session A, 9:00 am – 12:30 pm, Room 5: Samberg Conference Center, MIT]

Investigations of past and recent earthquake damage have illustrated that the building structures are vulnerable to severe damage and/or collapse during moderate to strong ground motion. Among the possible structural damages, seismic... more

Investigations of past and recent earthquake damage have illustrated that the building
structures are vulnerable to severe damage and/or collapse during moderate to strong ground motion. Among the possible structural damages, seismic induced pounding has been commonly observed in several earthquakes. A parametric study on buildings pounding response as well as proper seismic hazard mitigation practice for adjacent buildings is carried out. Three categories of recorded earthquake excitation are used for input. The effect of impact is studied using linear and nonlinear contact force model for different separation distances and compared with nominal model without pounding consideration. Pounding produces acceleration and shear at various story levels that are greater than those obtained from the no pounding case, while the peak drift depends on the input excitation characteristics. Also, increasing gap width is likely to be effective when the separation is sufficiently wide practically to eliminate contact.

From his earliest work forward, Merleau-Ponty attempted to develop a new ontology of nature that would avoid the antinomies of realism and idealism by showing that nature has its own endogenous sense which is prior to reflection. The key... more

From his earliest work forward, Merleau-Ponty attempted to develop a new ontology of nature that would avoid the antinomies of realism and idealism by showing that nature has its own endogenous sense which is prior to reflection. The key to this new ontology was the concept of form, which he appropriated from Gestalt psychology. However, Merleau-Ponty struggled to give a positive characterization of the phenomenon of form which would clarify its ontological status. Evan Thompson has recently taken up Merleau-Ponty’s ontology as the basis for a new, “enactive” approach to cognitive science, synthesizing it with concepts from dynamic systems theory and Francisco Varela’s theory of autopoiesis. However, Thompson does not quite succeed in resolving the ambiguities in Merleau-Ponty’s account of form. This article builds on an indication from Thompson in order to propose a new account of form as asymmetry, and of the genesis of form in nature as symmetry-breaking. These concepts help us to escape the antinomies of Modern thought by showing how nature is the autoproduction of a sense which can only be known by an embodied perceiver.

Modern Remotely Piloted Aircraft Systems (RPAS) employ a variety of sensors and multi-sensor data fusion techniques to provide advanced functionalities and trusted autonomy in a wide range of mission-essential and safety-critical tasks.... more

Modern Remotely Piloted Aircraft Systems (RPAS) employ a variety of sensors and multi-sensor data fusion techniques to provide advanced functionalities and trusted autonomy in a wide range of mission-essential and safety-critical tasks. In particular, Navigation and Guidance Systems (NGS) for small RPAS require a typical combination of lightweight, compact and inexpensive sensors to satisfy the Required Navigation Performance (RNP) in all flight phases. In this paper, the synergies attainable by the combination of Global Navigation Satellite System (GNSS), Micro-Electromechanical System based Inertial Measurement Unit (MEMS-IMU) and Vision-Based Navigation (VBN) sensors are explored. In case of VBN, an appearance-based navigation technique is adopted and feature extraction/optical flow methods are employed to estimate the navigation parameters during precision approach and landing phases. A key novelty of the proposed approach is the employment of Aircraft Dynamics Models (ADM) augmentation to compensate for the shortcomings of VBN and MEMS-IMU sensors in high-dynamics attitude determination tasks. To obtain the best estimates of Position, Velocity and Attitude (PVA), different sensor combinations are analysed and dynamic Boolean Decision Logics (BDL) are implemented for data selection before the centralised data fusion is accomplished. Various alternatives for data fusion are investigated including a traditional Extended Kalman Filter (EKF) and a more advanced Unscented Kalman Filter (UKF). A novel hybrid controller employing fuzzy logic and Proportional-Integral-Derivative (PID) techniques is implemented to provide effective stabilization and control of pitch and roll angles. After introducing the key mathematical models describing the three NGS architectures: EKF based VBN-IMU-GNSS (VIG) and VBN-IMU-GNSS-ADM (VIGA) and UKF based Enhanced VIGA (EVIGA), the system performances are compared in a small RPAS integration scheme (i.e., AEROSONDE RPAS platform) exploring a representative cross-section of the aircraft operational flight envelope. A dedicated ADM processor (i.e., a local pre-filter) is adopted in the EVIGA architecture to account for the RPAS maneuvering envelope in different flight phases (assisted by a maneuver identification algorithm), in order to extend the ADM validity time across all segments of the RPAS trajectory. Simulation results show that the VIG, VIGA and EVIGA systems are compliant with ICAO requirements for precision approach down to CAT-II. In all other flight phases, the VIGA system shows improvement in PVA data output with respect to the VIG system. The EVIGA system shows the best performance in terms of attitude data accuracy and a significant extension of the ADM validity time is achieved in this configuration.

Mecânica de estruturas unidimensionais

Book/e-book by J. B. Owens

Dynamical systems theories describe a wide range of theoretical orientations in cognitive science. In this chapter we focus on a particular formulation of dynamical systems theory that provides a strong theoretical basis for some of the... more

Dynamical systems theories describe a wide range of theoretical orientations in cognitive science. In this chapter we focus on a particular formulation of dynamical systems theory that provides a strong theoretical basis for some of the claims made by 4E approaches to cognition. In particular, the target dynamical systems approaches depend on two hypotheses. First, the interaction hypothesis states that the states and behaviors of any entity in a cognitive system are highly dependent on the states and behaviors of some other entity or set of entities. Second, the openness hypothesis states that cognitive systems only persist in the context of other systems. Taken together, these hypotheses entail that the boundaries of cognitive systems should not be taken for granted, and that there are both metrics and reasons for empirically investigating how cognitive systems may be bounded and how those boundaries might change.

Early research on new product development (NPD) has produced descriptive frameworks and models that view the process as a linear system with sequential and discrete stages. More recently, recursive and chaotic frameworks of NPD have been... more

Early research on new product development (NPD) has produced descriptive frameworks and models that view the process as a linear system with sequential and discrete stages. More recently, recursive and chaotic frameworks of NPD have been developed, both of which acknowledge that NPD progresses through a series of stages, but with overlaps, feedback loops, and resulting behaviors that resist reductionism and linear analysis. This article extends the linear, recursive, and chaotic frameworks by viewing NPD as a complex adaptive system (CAS) governed by three levels of decision making - in-stage, review, and strategic - and the accompanying
decision rules. The research develops and presents propositions that predict how the configuration and organization of NPD decision-making agents will influence the potential for three mutually dependent CAS phenomena: nonlinearity, selforganization, and emergence. Together these phenomena underpin the potential for NPD process adaptability and congruence. To support and to verify the propositions, this study uses comparative case studies, which show that NPD process
adaptability occurs and that it is dependent on the number and variety of agents, their corresponding connections and interactions, and the ordering or disordering effect of the decision levels and rules. Thus, the CAS framework developed within this article maintains a fit among descriptive stance, system behavior, and innovation type, as it considers individual NPD processes to be capable of switching or toggling between different behaviors - linear to chaotic - to produce corresponding innovation outputs that range from incremental to radical in accord with market expectations.

The current rise of neurodevelopmental disorders poses a critical need to detect risk early in order to rapidly intervene. One of the tools pediatricians use to track development is the standard growth chart. The growth charts are... more

The current rise of neurodevelopmental disorders poses a critical need to detect risk early in order to rapidly intervene. One of the tools pediatricians use to track development is the standard growth chart. The growth charts are somewhat limited in predicting possible neurodevelopmental issues. They rely on linear models and assumptions of normality for physical growth data – obscuring key statistical information about possible neurodevelopmental risk in growth data that actually has accelerated, non-linear rates-of-change and variability encompassing skewed distributions. Here, we use new analytics to profile growth data from 36 newborn babies that were tracked longitudinally for 5 months. By switching to incremental (velocity-based) growth charts and combining these dynamic changes with underlying fluctuations in motor performance – as the transition from spontaneous random noise to a systematic signal – we demonstrate a method to detect very early stunting in the development of voluntary neuromotor control and to flag risk of neurodevelopmental derail.

A robotic arm having two links is considered in this report for modeling and control. First the dynamic model of the robot is obtained using the so-called Lagrange equation, then a robust control strategy based on the conventional sliding... more

A robotic arm having two links is considered in
this report for modeling and control. First the dynamic model
of the robot is obtained using the so-called Lagrange equation,
then a robust control strategy based on the conventional sliding
mode control is introduced to control the motion of the robot at
specific position for pick and place tasks along with PID control
scheme. The results of the two controllers are compared. From
the simulation results the SMC is found to be superior to the PID
controller in term of fast and robust response yet with higher
control input. High join speeds are observed in case of SMC
which are related to the high control signals.

The aim of this paper was to determine whether fractal processes underlie the dynamics of self-esteem and physical self. Twice a day for 512 consecutive days, four adults completed a brief inventory measuring six subjective dimensions:... more

The aim of this paper was to determine whether fractal processes underlie the dynamics of self-esteem and physical self. Twice a day for 512 consecutive days, four adults completed a brief inventory measuring six subjective dimensions: global self-esteem, physical self-worth, physical condition, sport competence, attractive body, and physical strength. The obtained series were submitted to spectral analysis, which allowed their classification as fractional Brownian motions. Three fractal analysis methods (Rescaled Range analysis, Dispersional analysis, and Scaled Windowed Variance analysis) were then applied on the series. These analyses yielded convergent results and evidenced long-range correlation in the series. The self-esteem and physical self series appeared as anti-persistent fractional Brownian motions, with a mean Hurst exponent of 0.21. These results reinforce the conception of self-perception as the emergent product of a dynamical system composed of multiple interacting e...

The effects of blast loading on structures can be very dangerous: damages and failures are expected 8 with serious threats to structural safety and human life. Materials stresses and strains are often pushed to the limit and the modelling... more

The effects of blast loading on structures can be very dangerous: damages and failures are expected 8 with serious threats to structural safety and human life. Materials stresses and strains are often pushed to the limit and the modelling of these phenomena can be very complex. In order to design blast-resistant structures it is very important to determine what are the key parameters of this problem. This paper presents a reliability and parametric analysis of the response of Reinforced Concrete (RC) beams under blast loads. The main aim is to highlight the key parameters of the problem in order to produce information useful for the design of reliable blast-resistant RC structures. The beam has been idealised as an equivalent SDOF system, in which strain-rate effects are accounted for. This approach is convenient from a computational point of view and it has been validated by a direct comparison with a more sophisticated finite element model and with experimental results found in literature. Then a sensitivity analysis of the parameters involved in beam response under blast load has been developed. Slenderness (which has a direct effect on stiffness) and peak load prove to be the most important parameters, but span length (which has an important influence on the mass) is also a key parameter. Other variables such as concrete strength and reinforcement ratio do not seem to have a strong correlation with the beam response.

This paper has two aims. First, we study the impact of oil price variables (change and volatility) on stock market returns under regime shifts in the case of Gulf Cooperation Council (GCC) countries. We employ a Markov regime-switching... more

This paper has two aims. First, we study the impact of oil price variables (change and volatility)
on stock market returns under regime shifts in the case of Gulf Cooperation Council (GCC)
countries. We employ a Markov regime-switching model to generate regime probabilities for
oil market variables. We use two state Markov switching models: crisis regime and non-crisis
regime. Second, we investigate the non-linear relationship among oil price, interest rates and
inflation rates before and during the subprime crisis. We consider several Archimedean copula
models with different tail dependence structures, namely, Gumbel, Clayton and Frank copulas.
We find evidence that the relationship between GCC stock market returns and OPEC oil market
volatility is regime dependent (excluding Oman in the low volatility state). We also find that
the dependence structure between inflation rates and crude oil prices is asymmetric and
orients toward the upper side during the recent financial crisis. Furthermore, we find evidence
of significant symmetric dependence between crude oil prices and the short-term interest rate
during the financial crisis. These paper's results have practical significance and important
implications for both GCC economic policy and financial stability.

This study describes numerically, the interdependency between several seismic acceleration parameters and diverse structural damage indices. Peak ground motion, spectral and energy parameters are used for characterising the seismic... more

This study describes numerically, the interdependency between several seismic acceleration parameters and diverse structural damage indices. Peak ground motion, spectral and energy parameters are used for characterising the seismic excitation. On the other hand both, structural and nonstructural damage is considered, expressed by the modified Park/Ang overall structural damage index (OSDI), the maximum interstory drift (ISD) and the maximum floor acceleration. After the numerical evaluation of several seismic parameters, nonlinear dynamic analyses are conducted to furnish the structural damage status. The degree of the interrelationship between the seismic parameters and the damage indices is provided by correlation coefficients. The investigation is carried out for a reinforced concrete plane frame system designed after Eurocodes 2 and 8 (EC2, EC8) and the aim is to determine the characteristics of the accelerograms that exhibit the strongest influence on structural and nonstructural damages. The numerical results have shown, that peak ground motion seismic parameters provide poor or fair correlation with the OSDI, whereas the spectral and energy parameters provide good correlation. Furthermore, the central period and the strong motion duration after Trifunac/Brady exhibit poor correlation with the OSDI. All these results give reason to recommend the spectra and energy related seismic intensity parameters as reliable descriptors of the seismic damage potential.

A concept and methodology derived from an animal model provided the framework for a study of rituals in obsessive compulsive disorder (OCD) patients and yielded objective and observable criteria applicable for compulsive rituals across... more

A concept and methodology derived from an animal model provided the framework for a study of rituals in obsessive compulsive disorder (OCD) patients and yielded objective and observable criteria applicable for compulsive rituals across patients. The employed ethological approach should be able to reveal and identify a common structure underlying OCD rituals, pointing to shared psychopathology. Eleven OCD rituals performed by patients in their own home were videotaped and compared with the behaviour of healthy individuals instructed to perform the same rituals. The videotaped rituals were deconstructed into visits to specific locations or objects (ritual space), and to the acts performed at each location/object (ritual basic components). Quantitative analyses revealed that compulsiveness emanates from the expansion of repeats for some acts and visits, and from the addition of superfluous act types. Best discrimination between OCD and control rituals (90.9% success) was provided by th...

This paper presents a comparative study of the Colpitts oscillator circuit using circuit simulations and experimental results. Different techniques of dynamical systems theory like time series plots, phase portraits and Lyapunov exponents... more

This paper presents a comparative study of the Colpitts oscillator circuit using circuit simulations and experimental results. Different techniques of dynamical systems theory like time series plots, phase portraits and Lyapunov exponents were employed. The time series plots and phase portraits for different state variables of Colpitts oscillator circuit, obtained from PSpice simulation and experimental implementation, were compared with each other. This comparison showed that both the results are identical. It is evident that chaotic Colpitts oscillator exhibited periodic and aperiodic behavior for different values of the circuit parameters.