Control and Synchronization of Chaotic/Hyperchaotic Systems Research Papers (original) (raw)

The synchronization of coupled chaotic systems represents a fundamental example of self organization and collective behavior. This well-studied phenomenon is classically characterized in terms of macroscopic parameters , such as Lyapunov exponents, that help predict the system's transitions into globally organized states. However, the local, microscopic, description of this emergent process continues to elude us. Here we show that at the microscopic level, synchronization is captured through a gradual process of topological adjustment in phase space, in which the strange attractors of the two coupled systems continuously converge, taking similar form, until complete topological synchronization ensues. We observe the local nucleation of topological synchronization in specific regions of the system's attractor, providing early signals of synchrony, that appear significantly before the onset of complete synchronization. This local synchronization initiates at the regions of the attractor characterized by lower expansion rates, in which the chaotic trajectories are least sensitive to slight changes in initial conditions. Our findings offer a fresh and novel description of synchronization in chaotic systems, exposing its local embryonic stages that are overlooked by the currently established global analysis. Such local topological synchronization enables the identification of configurations where prediction of the state of one system is possible from measurements on that of the other, even in the absence of global synchronization.

This paper aims at synchronization and anti-synchronization between Lu chaotic system, a member of unified chaotic system, and recently developed Bhalekar–Gejji chaotic system, a system which cannot be derived from the member of unified chaotic system. These synchronization and anti-synchronization have been achieved by using nonlinear active control since the parameters of both the systems are known. Lyapunov stability theory is used and required condition is derived to ensure the stability of error dynamics. Controller is designed by using the sum of relevant variables in chaotic systems. Simulation results suggest that proposed scheme is working satisfactorily.

- by PIYUSH PRATAP SINGH and +2
- •
- Control and Synchronization of Chaotic/Hyperchaotic Systems

The International Journal of Chaos, Control, Modeling and Simulation is a Quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of Chaos Theory, Control Systems, Scientific Modeling and Computer Simulation. In the last few decades, chaos theory has found important applications in secure communication devices and secure data encryption. Control methods are very useful in several applied areas like Chaos, Automation, Communication, Robotics, Power Systems, and Biomedical Instrumentation. The journal focuses on all technical and practical aspects of Chaos, Control, Modeling and Simulation. The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on chaotic systems and applications, control theory, process control, automation, modeling concepts, computational methods, computer simulation and establishing new collaborations in these areas.

The International Journal of Chaos, Control, Modelling and Simulation is a Quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of Chaos Theory, Control Systems, Scientific Modelling and Computer Simulation. In the last few decades, chaos theory has found important applications in secure communication devices and secure data encryption. Control methods are very useful in several applied areas like Chaos, Automation, Communication, Robotics, Power Systems, and Biomedical Instrumentation. The journal focuses on all technical and practical aspects of Chaos, Control, Modelling and Simulation. The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on chaotic systems and applications, control theory, process control, automation, modelling concepts, computational methods, computer simulation and establishing new collaborations in these areas.

– This work presents synchronization between two different chaotic systems by a high gain observer. We have studied the synchronization problem between Rössler system and a new chaotic system recently developed in the literature. A theoretical frame is provided in order to show the convergence characteristics of the proposed observer under some satisfied assumptions. The observer performances are verified by numerical simulations.

In this paper, a scheme of global anti-synchronization between two identical newly developed
Bhalekar–Gejji chaotic system is proposed. This anti-synchronization scheme is achieved by
using nonlinear active control since the parameters of both the systems are known and states
are measurable. Lyapunov stability theory is used to ensure stability of error dynamics.
Controller is designed by using the sum of relevant variables in master and slave chaotic
systems. Simulation results reveal that proposed scheme is working satisfactorily.

- by Jay Singh and +2
- •
- Control and Synchronization of Chaotic/Hyperchaotic Systems

n this paper, design of SMC scheme based controller is proposed for synchronization of two different hyperchaotic systems. Synchronization is achieved using the Lyapunov stability theory. A proportional integral (PI) switching surface is used to ensure the stability of the closed-loop error dynamics in sliding motion. This SMC scheme is effective and guarantees the occurrence of sliding motion and achieves synchronization of master hyperchaotic Xu and slave hyperchaotic Lorenz system. Combinations of two different hyperchaotic systems are used for the synchronization reflecting the novelty of paper. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed control strategy.

- by PIYUSH PRATAP SINGH and +1
- •
- Control and Synchronization of Chaotic/Hyperchaotic Systems
- by PIYUSH PRATAP SINGH and +2
- •
- Control and Synchronization of Chaotic/Hyperchaotic Systems

Data security has become an important concern for communication through an insecure channel because the information transferred across the networks has a large chance of unauthorized access. The available encryption algorithms that are primarily used for text data may not be suitable for multimedia data such as sound. Hyperchaotic systems are generally proposed as a solution to multimedia encryption, because of their random properties and the high sensitivity of initial conditions and system parameters. In this paper, audio data encryption with different dimensional hyperchaotic systems has been presented. The proposed hyperchaotic systems exhibit excellent chaotic behavior. To demonstrate its application to the processing of multimedia encryption, the three systems are applied with an algorithm based on the key generation from the initial conditions for encryption and de-cryption process. The results of encryption, decryption and statistical analysis of the audio data show that the proposed cryptosystem has excellent encryption performance, high sensitivity to security keys and can be applied for secure real-time encryption.

This paper derives new results for the adaptive control and synchronization design of the Shimizu-Morioka chaotic system (1980), when the system parameters are unknown. First, we build an adaptive controller to stabilize the Shimizu-Morioka chaotic system to its unstable equilibrium at the origin. Then we build an adaptive synchronizer to achieve global chaos synchronization of the identical Shimizu-Morioka chaotic systems with unknown parameters. The results derived for adaptive control and adaptive synchronization for the Shimizu-Morioka chaotic system have been proved using adaptive control theory and Lyapunov stability theory. Numerical simulations have been depicted to demonstrate the effectiveness of the adaptive control and synchronization schemes derived in this paper for the Shimizu-Morioka chaotic system.

This study illustrates presents a set of the Long – Term Geoelectric Potential (LTGP) measurements that are collected for experimental investigation in Western Greece during a five–year period (1993 – 1997). During this period, many major destructive earthquake events occurred hat caused human casualties and extended material damages. The ollection and processing of geoelectric measurements was done by an automated data acquisition system at the Seismological Laboratory of the University of Patras, Greece. This novel study considers seismic activity of this area as a typical linear dynamic system and the dynamic relationship between the magnitude of earthquakes and Long – Term Geoelectric Potential signals is inferred by the Recursive Least Square algorithm. The results are encouraging and show that linear dynamic systems, which are widely used in modern control theory, can describe efficiently the dynamic behavior of seismic activity and become a useful interpretative tool of seismic phenomenon.

Hybrid synchronization based on the active control theory between two different chaotic systems, i.e. Lu and Bhalekar-Gejji is reported in this paper. Lu chaotic system is taken as master and Bhalekar-Gejji chaotic system as slave. Stabilization of error dynamics is achieved by satisfying the Lyapunov stability conditions. Control is designed by using the relevant variables of master and slave systems. Simulation is presented for verification of proposed scheme.

- by PIYUSH PRATAP SINGH and +2
- •
- Control and Synchronization of Chaotic/Hyperchaotic Systems

This paper investigates the design problem of adaptive controller and synchronizer for the Qi-Chen system (2005), when the system parameters are unknown. First, we build an adaptive controller to stabilize the Qi-Chen chaotic system to its unstable equilibrium at the origin. Then we build an adaptive synchronizer to achieve global chaos synchronization of the identical Qi-Chen chaotic systems with unknown parameters. The results derived for adaptive stabilization and adaptive synchronization for the Qi-Chen chaotic system are established using adaptive control theory and Lyapunov stability theory. Numerical simulations have been shown to demonstrate the effectiveness of the adaptive control and synchronization schemes derived in this paper for the Qi-Chen chaotic system.

In this paper synchronization of two different chaotic systems is proposed using Sliding Mode Control scheme. Lu chaotic system is used as master system and Bhalekar-Gejji chaotic system is used as slave system. Convergence of the synchronizing error is achieved using the Lyapunov stability theory. Synchronization of master and slave system is achieved using the PI (Proportional-Integral) switching surface of the sliding mode control scheme. Finally, numerical simulations are proposed to demonstrate the effectiveness of proposed synchronization strategy.

- by PIYUSH PRATAP SINGH and +1
- •
- Control and Synchronization of Chaotic/Hyperchaotic Systems

This paper investigates the anti-synchronization of identical hyperchaotic Xu systems (Xu, Cai and Zheng, 2009) via sliding mode control. The stability results derived in this paper for the anti-synchronization of identical hyperchaotic Xu systems are established using Lyapunov stability theory. Since the Lyapunov
exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve anti- synchronization of the identical hyperchaotic Xu systems. Numerical simulations are shown to illustrate and validate the anti-synchronization schemes derived in this paper for the identical hyperchaotic Xu systems.

Vehicular Ad-hoc Networks (VANET) have great potential to enable different applications associated with safety and infotainment. The feasibility of using the Chua-based synchronous cryptography system (cryptosystem) for VANET's security is investigated in the present paper. Two vehicles with synchronized chaotic generators is considered to encryption and decryption scenario. According to IEEE standards, the chaotic encryption and OFDM techniques are combined in the proposed scheme. The complexity of the proposed system is low and the numerical simulations show that by sending Cipher-text trough an AWGN channel using the proposed scheme, we can maintain BER at a desired level and improve the security of the communication system.

In this paper, we apply adaptive control method to derive new results for the global chaos synchronization of 4-D chaotic systems, viz. identical Lorenz-Stenflo(LS) systems (Stenflo, 2001), identical Qi systems (Qi, Chen and Du, 2005) and non-identical LS and Qi systems. In this paper, we shall assume that the parameters of both master and slave systems are unknown and we devise adaptive control schemes for synchronization using the estimates of parameters for both master and slave systems. Our adaptive synchronization schemes derived in this paper are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the adaptive control method is very effective and convenient to synchronize identical and non-identical LS and Qi systems. Numerical simulations are shown to demonstrate the effectiveness of the proposed adaptive synchronization schemes for the identical and non-identical, uncertain LS and Qi 4-D chaotic systems.

This paper addresses the anti-synchronization problem of two Bhalekar-Gejji Chaotic
systems in the presence of unknown system parameters. Based on Lyapunov stability
theory an adaptive control law is devised to make the states of two identical BhalekarGejji chaotic systems with unknown system parameters asymptotically synchronized.
Finally, numerical simulations are presented to show the effectiveness of the proposed
chaos anti-synchronization scheme and the objective.

- by PIYUSH PRATAP SINGH and +1
- •
- Adaptive Control, Control and Synchronization of Chaotic/Hyperchaotic Systems

We study networks of diffusively time-delay coupled oscillatory units and we show that networks with certain symmetries can exhibit a form of incomplete synchronization called partial synchronization. We present conditions for the existence and stability of partial synchronization modes in networks of oscillatory units that satisfy a semipassivity property and have convergent internal dynamics.

Human beings have adopted tools, pets, technology, especially computer science and Deep Learning (DL) in Virtual Intelligent Assistants (VIA). Digital technical assistance systems that predict the future in culture, business and politics are now in demand. The experience gained with Deep Learning (DL) is to be mapped to a model of a Virtual Intelligent Assistant (VIA) for social science, culture and economics. The Deep Learning (DL) model is based on an Artificial Neural Network (ANN) that contains artificial nodes (simplified nerve cells) and artificial neurons (simplified synapses). The special feature is that the artificial nodes (simplified nerve cells) are arranged in several hidden layers with autonomous filtering processes. Autonomous filters in the artificial nodes (simplified nerve cells) require rules that are static, i.e. time-invariant. For this purpose, the Logia of the Gospel of Thomas are proposed. It seems that the Gospel of Thomas summarizes insights and experiences from 80 thousand years of human history in 114 Logia. They are shown in outline points 1 to 114. Ultimately, the weight of the interaction determines that artificial neurons (simplified synapses) are represented in the model, as an entered statement at the output of the Artificial Neural Network (ANN) is to be understood. The boundaries between the machine, the individual and society continue to dissolve in the chaotic. It would be nice if world knowledge, as collected by the company Cyrorp, could be modelled. Instead of a model of world knowledge, Eva Soyah proposes the collection of Logia in subdivision points 1 to 114 and Permanent Truths from item 115.

- by Eva Soyah
- •
- Community Development, Theory of Mind, Transhumanism, Presuppositions

The coexistence of infinitely many attractors is called extreme multistability in dynamical systems. In coupled systems, this phenomenon is closely related to partial synchrony and characterized by the emergence of a conserved quantity. We propose a general design of coupling that leads to partial synchronization, which may be a partial complete synchronization or partial antisynchronization and even a mixed state of complete synchronization and antisynchronization in two coupled systems and, thereby reveal the emergence of extreme multistability. The proposed design of coupling has wider options and allows amplification or attenuation of the amplitude of the attractors whenever it is necessary. We demonstrate that this phenomenon is robust to parameter mismatch of the coupled oscillators.

- by Chittaranjan Hens and +1
- •
- Dynamical systems and Chaos, Control and Synchronization of Chaotic/Hyperchaotic Systems

This paper presents the new Lorenz unlike chaotic attractor which is constructed by a three non linear first order differential equations. These equations are arranged in a three dimensional autonomous systems. The dynamic behavior of the new chaotic system is shown such as time series, strange attractors, and bifurcations. Numerical experience also shows that when the parameter 'd' is varied, the global non linear amplitude is also varying. The paper ends with some possible research and development recommendations.

This paper investigates the global chaos synchronization of identical Shimizhu-Morioka chaotic systems (Shimizu and Morioka, 1980) by sliding mode control. The stability results derived in this paper for the complete synchronization of identical Shimizu-Morioka chaotic systems are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve global chaos synchronization of the identical Shimizu-Morioka chaotic systems. Numerical simulations are shown to illustrate and validate the synchronization schemes derived in this paper for the identical Shimizu-Morioka systems.

Heart Rate Variability (HRV) plays an important role for reporting several cardiological and noncardiological
diseases. Also, the HRV has a prognostic value and is therefore quite important in modelling the cardiac risk. The nature of the HRV is chaotic, stochastic and it remains highly controversial. Because the HRV has utmost importance, it needs a sensitive tool to analyze the variability. In previous work,Rosenstein and Wolf had used the Lyapunov exponent as a quantitative measure for HRV detection sensitivity. However, the two methods diverge in determining the HRV sensitivity. This paper introduces a modification to both the Rosenstein and Wolf methods to overcome their drawbacks. The introduced
Mazhar-Eslam algorithm increases the sensitivity to HRV detection with better accuracy.

This paper derives new results for the design of sliding mode controller for the global chaos synchronization of identical hyperchaotic Lorenz systems (Jia, 2007). The synchronizer results derived in this paper for the complete chaos synchronization of identical hyperchaotic systems are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve global chaos synchronization of the identical hyperchaotic Lorenz systems. Numerical simulations are shown to illustrate and validate the synchronization schemes derived in this paper for the identical hyperchaotic Lorenz systems.

In this paper an analytic approach is devised to re
present, and study the behavior of, nonlinear dynam
ic
chaotic Genesio system using general nonlinear moda
l representation. In this approach, the original
nonlinear ordinary differential equations (ODEs) of
model transforms to a sequence of linear time-
invariant ODEs. By solving the proposed linear ODEs
sequence, the exact solution of the original
nonlinear problem is determined in terms of uniform
ly convergent series. Also an efficient algorithm w
ith
low computational complexity and high accuracy is p
resented to find the approximate solution. Simulati
on
results indicate the effectiveness of the proposed
method.

- by Arman Sargolzaei and +1
- •
- Control and Synchronization of Chaotic/Hyperchaotic Systems

In
chaos theory, the problem
anti
-
synchronization of chaotic system
s deals with
a pair of chaotic systems
called
drive and response
systems. In this problem, the
design goal is
to drive the sum of their respective
states to zero asymptotically.
This problem gets even more complicated and requires special attention when
the parameters of the drive and response systems are unknown.
This paper
uses adaptive control th
eory
and Lyapunov stability theory to derive
new results for the anti
-
synchronization of hyperchaotic
W
ang
system (200
8
) and hyperchaotic
Li
system (20
05
) with uncertain p
arameters.
Hyperchaotic systems are
nonlinear
dynamical
systems
exhibiting chaotic be
haviour
with
two or more
positive Lyapunov exponent
s.
The hyperchaotic systems
have applications in areas like
oscillators, lasers,
neural networks, encryption,
secure transmission and
secure
communication.
The main results derived in this paper are
validated and
demonstrated
with MATLAB
s
imulations
.

The Lotka-Volterra equations are a system of equations proposed to provide a simplified model of twospecies
predator-prey population dynamics. In this paper, we investigate the problem of adaptive chaos
control and synchronization of a generalized Lotka-Volterra system discovered by Samardzija and Greller
(1988). The Samardzija-Greller model is a two-predator, one-prey generalization of the Lotka-Volterra
system. First, adaptive control laws are designed to stabilize the generalized Lotka-Volterra system to its
unstable equilibrium point at the origin based on the adaptive control theory and Lyapunov stability
theory. Then adaptive control laws are derived to achieve global chaos synchronization of identical
generalized Lotka-Volterra systems with unknown parameters. Numerical simulations are shown to
validate and demonstrate the effectiveness of the proposed adaptive control and synchronization schemes
for the generalized Lotka-Volterra system.

Der Mensch hat sich Werkzeuge, Haustiere, die Technik, insbesondere die Informatik und das Deep Learning (DL) in Virtuellen Intelligenten Assistenten (VIA) zu eigen gemacht. Nun sind digitale technische Assistenzsysteme, die die Zukunft in Kultur, Wirtschaft und Politik vorhersagen, gefragt. Die bisher gesammelten Erfahrungen mit Deep Learning (DL) sollen auf ein Modell eines Virtuellen Intelligenten Assistenten (VIA) für die Gesellschaftswissenschaft, Kultur und der Volkswirtschaft abgebildet werden. Das Modell des Deep Learning (DL) basiert auf einem Künstlichen Neuronalen Netzwerk (KNN), das künstliche Knoten (vereinfachte Nervenzellen) und künstliche Neuronen (vereinfachte Synapsen) enthält. Die Besonderheit ist, dass die künstlichen Knoten (vereinfachten Nervenzellen) in mehreren versteckten Ebenen (Hidden Layers) mit autonomen Filterprozessen angeordnet sind. Für autonome Filter in den künstlichen Knoten (vereinfachten Nervenzellen) werden Regeln benötigt, die statisch d.h. zeitinvariant sind. Dafür werden die Logien des Thomasevangeliums vorgeschlagen. Es sieht so aus, dass das Thomasevangelium Erkenntnisse und Erfahrungen aus 80 Tausend Jahren Menschheitsgeschichte in 114 Logien zusammenfasst. Sie sind in den Gliederungspunkten 1 bis 114 dargestellt. Letztlich entscheidet das Gewicht der Wechselwirkung, dass durch künstliche Neuronen (vereinfachte Synapsen) im Modell repräsentiert wird, wie eine eingegebene Aussage am Ausgang des Künstlichen Neuronalen Netzwerkes (KNN) zu verstehen ist. Die Grenzen zwischen Maschine, Individuum und Gesellschaft lösen sich im Chaotischen immer weiter auf. Es wäre schön, wenn das Weltwissen, so wie es die Fa. Cyrorp sammelt, modellierbar ist. Anstelle eines Modells des Weltwissens schlägt Eva Soyah die Sammlung der Logien in den Gliederungspunkten 1 bis 114 und Zeitlosen Wahrheiten ab Gliederungspunkt 115 vor.

- by Eva Soyah
- •
- Computer Science, Social Sciences, Community Development, Theory of Mind

This work studies the dynamics, control and synchronization of hyperchaotic Lorenz-stenflo system and its application to secure communication. The proposed designed nonlinear feedback controller control and globally synchronizes two identical Lorenz-stenflo hyperchaotic systems evolving from different initial conditions with unknown parameters. Adaptive synchronization results were further applied to secure communication. The numerical simulation results were presented to verify the effectiveness of the designed nonlinear controller and its success in secure communication application.

This paper investigates hybrid synchronization between two non-identical hyperchaotic systems using sliding mode control (SMC) strategy. Hyperchaotic Lu system is considered as master and hyperchaotic Bao system as slave system. The stability results are established using PI (Proportional Integral) switching surface and Lyapunov stability theory for hybrid synchronization scheme. SMC is used to reduce the influence of disturbance and improve system robustness which helps to achieve the convergence of error dynamics easily. Finally, numerical simulations are performed to demonstrate the effectiveness of proposed hybrid synchronization strategy of two non-identical hyperchaotic systems.

- by PIYUSH PRATAP SINGH and +1
- •
- Control and Synchronization of Chaotic/Hyperchaotic Systems

This With the advance of Web Services technologies and the emergence of Web Services into the information space, tremendous opportunities for empowering users and organizations appear in various application domains including electronic commerce, travel, intelligence information gathering and analysis, health care, digital government, etc. In fact, Web services appear to be s solution for integrating distributed, autonomous and heterogeneous information sources. However, as Web services evolve in a dynamic environment which is the Internet many changes can occur and affect them. A Web service is affected when one or more of its associated information sources is affected by schema changes. Changes can alter the information sources contents but also their schemas which may render Web services partially or totally undefined. In this paper, we propose a solution for integrating information sources into Web services. Then we tackle the Web service synchronization problem by substituting the affected
information sources. Our work is illustrated with a healthcare case study.

This paper investigates the hybrid synchronization of identical Pan systems (Pan, Xu and Zhou, 2010) by sliding mode control. In hybrid synchronization of chaotic systems, one part of the master and slave systems is completely synchronized, while the other part is anti-synchronized. The coexistence of complete and anti-synchronization enhances the security of the communication devices using chaotic systems. The stability results derived in this paper for the hybrid synchronization of identical Pan systems are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve hybrid synchronization of the identical Pan systems. Numerical simulations are shown to illustrate and validate the hybrid synchronization schemes derived in this paper for the identical Pan systems.

The paper proposes a sliding mode control strategy-based scheme for achieving anti-
synchronization between two coupled non-linear chaotic systems. The method works irrespective
of whether the systems under consideration possess or lack inverse symmetry. Using a linear sliding
surface, a sliding mode control input and a non-linear coupling function are designed that synchro-
nizes the systems antiphase. Finite-time convergence of the method is established. The controller is
also robust to all forms of bounded perturbations and this robustness can be easily achieved by tun-
ing of a single controller parameter and introduction of a control vector. The controller is also made
chattering-free by producing a continuous analogue of the discontinuous control input. The effec-
tiveness of the method is established by implementing it to antisynchronize chaotic Sprott systems
and Rossler systems. The results are also verified through numerical simulation work.

This paper investigates the global chaos synchroniz
ation of identical Qi four-wing chaotic systems (Qi
et
al., 2008), identical Liu four-wing chaotic systems
(Liu, 2009) and identical Wang chaotic systems (Wa
ng
et al., 2009). The stability results derived in thi
s paper for the complete synchronization of the thr
ee pairs
of identical four-wing chaotic systems are establis
hed using Lyapunov stability theory. Since the Lyap
unov
exponents are not required for these calculations,
the sliding mode control method is very effective a
nd
convenient to achieve global chaos synchronization
of the four-wing chaotic systems. Numerical
simulations are shown to illustrate and validate th
e synchronization schemes derived in this paper for
the
identical four-wing chaotic systems