Dynamics of a Nonlinear Digital Resonator inFree Running and Injection Synchronized Mode:A Simulation Study (original) (raw)
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Synchronization Response of an Indirectly Coupled Nonlinear Digital Resonator -A Simulation Study
2014
In modern communication technology, the preference of digital systems compared to their analog counterparts is well documented in literature [1-3]. Digital systems have flexibility in design, reliability in long time application, negligible dc drift and easy implementation possibility in IC technology. So researchers and the system designers are interested in designing different digital systems which could perform the jobs of already available analog systems [4, 5]. In digital signal processing digital filters are most important elements. They find application in removing undesirable co-channel signals and additive noise, in spectral shaping etc. [1]. Digital Resonators (DRs) belong to a group of second order digital filters that exhibit natural oscillations depending upon its design parameter values and they can be used as signal sources. DRs are used as digital frequency synthesizers [1]. However, they cannot be synchronized to external signal as they are basically linear systems. Modifications of the DR with the introduction of controlled nonlinearities in the system make the system synchronizable to an external signal. Moreover presence of nonlinearity would enrich its dynamics. As for example the system exhibits bifurcation, chaos, quasi-periodicity etc. A discrete equivalent of DR having the nonlinearities of a Vander pol oscillator has been proposed by the authors [6]. In this paper, we consider two such nonlinear digital resonators (NDRs) in a uni-directionally coupled configuration and study the synchronization performance of the second NDR (consider as response system) both in stable periodic oscillation and chaotic oscillation of the first NDR (consider as driver system). Here the dynamics of the response NDR is controlled by parameter tuning with the help of an error signal generated by comparing the phases of the driver and the response NDRs and the principle of conventional phase locked loops is being used here for that indirect coupling. The design parameters of response system could have non-identical values from that of the driver. We have studied the synchronization response of the response NDR in a generalized sense and for this purpose, the auxiliary system method of nonlinear dynamics [7-9] have been followed. The paper has been organized as follows. In Section II, the difference equations describing the system dynamics for an isolated NDR and a cascaded NDR system have been formulated. The difference equations in terms of some error variables have been formulated at the end of this section to study the generalized synchronization (GS) between the driver and the response NDR. The results of numerical simulation on the dynamics of cascaded system have been given in Section III. A brief of simulation results regarding the dynamics of single NDR in presence of external forcing signal are given in first part of section III for completeness of discussion. Finally, we concluded with our findings and future implementation possibilities of the work in section IV. II. System equation formulation The dynamical behavior of a NDR has been studied in [6] numerically with the help of difference equation that describes the time evolution of the system. For the sake of completeness, we include the description of the structure and system equations of that work in subsection A and then we describe the structure of the cascaded system and formulate the corresponding system equations in subsection B. The subsection C describes the "auxiliary system" method through which the GS between two NDR is examined.
Nonlinear electronic circuit, Part II: synchronization in a chaotic MODEM scheme
Nonlinear Analysis: Theory, Methods & Applications, 2009
In this work we present a thorough investigation of the effect of noise (internal or external) on the synchronization of a drive-response configuration system (unidirectional coupling between two identical systems). Moreover, since in every practical implementation of a communication system, the transmitter and receiver circuits (although identical) operate under slightly different conditions it is essential to consider the case of the mismatch between the parameters of the transmitter and the receiver. In our work we consider the non-autonomous 2nd order nonlinear oscillator system presented in [G. Mycolaitis, A. Tamasevicious, A. Cenys, A. Namajunas, K. Navionis, A. N. Anagnostopoulos, Globally synchronizable non-autonomous chaotic oscillator, in: Proc. of 7th International Workshop on Nonlinear Dynamics of Electronic Systems, Denmark, July 1999, pp. 277-280] which is particularly suitable for digital communications.
Harmonic oscillations, routes to chaos and synchronization in a nonlinear emitter-receiver system
IEEE 60th Vehicular Technology Conference, 2004. VTC2004-Fall. 2004
This paper considers a model describing the dynamics of a Transmitter-receiver system in communication engineering. The bifurcation structure is analyzed to define the nature of the bifurcations exhibited by the system. One does found both the complex dynamical behavior of the system and its extreme sensitivity to tiny changes in the model parameters. Crisis, Period-doubling and Hopf bifurcation are also found. An analog simulation of the Transmitter-receiver system is carried out. Some experimental phase portraits are obtained. Both regular and chaotic modulations of the incoming message are done experimentally. A comparison of the results obtained from experimental and numerical analysis shows a very good agreement.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 1997
We stabilize unstable periodic orbits of a fast diode resonator driven at 10.1 MHz ͑corresponding to a drive period under 100 ns͒ using extended time-delay autosynchronization. Stabilization is achieved by feedback of an error signal that is proportional to the difference between the value of a state variable and an infinite series of values of the state variable delayed in time by integral multiples of the period of the orbit. The technique is easy to implement electronically and it has an all-optical counterpart that may be useful for stabilizing the dynamics of fast chaotic lasers. We show that increasing the weights given to temporally distant states enlarges the domain of control and reduces the sensitivity of the domain of control on the propagation delays in the feedback loop. We determine the average time to obtain control as a function of the feedback gain and identify the mechanisms that destabilize the system at the boundaries of the domain of control. A theoretical stability analysis of a model of the diode resonator in the presence of time-delay feedback is in good agreement with the experimental results for the size and shape of the domain of control. © 1997 American Institute of Physics. ͓S1054-1500͑97͒00104-3͔
Controlling chaos in nonlinear optical resonators
Chaos, Solitons & Fractals, 2000
This article presents an analytical method for controlling the chaos in two nonlinear bistable optical resonators. The devices are a bulk cavity ring oscillator and a nonlinear simple ®bre ring resonator. It is shown that there is a trade-o between¯exibility and controllability in such devices. For the ®rst time, as far as the authors are aware, theoretical studies have shown that by controlling the chaos within a bistable region it becomes possible to use a previously unstable device as a bistable resonator. Ó
pplication of Chaotic Synchronizatio n and Controlling Chaos to Communications
This thesis addresses two important issues that are applicable to chaotic communication systems: synchronization of chaos and controlling chaos. Synchronization of chaos is a naturally occurring phenomenon where one chaotic dynamical system mimics dynamical behavior of another chaotic system. This phenomenon can be used in chaotic communication system as a mechanism for information decoding whereas controlling chaos can be used to encode information into the dynamics of the system. Apart from this particular application, the phenomenon of chaotic synchronization is a popular topic of research, in general, and has attracted much attention within the scientific community. Controlling chaos is another potential engineering application. A unique property of controlling chaos is the ability to cause large long-term impact on the dynamics using arbitrarily small perturbations. This thesis is broken up into three chapters. The first chapter contains a brief introduction to the areas of research of the thesis work, as well as the summaries the work itself. The second chapter is dedicated to the study of a particular situation of chaotic synchronization which leads to a novel structure of the basin of attraction. This chapter also develops theoretical scalings applicable to these systems and compares results of our numerical simulations on three different chaotic systems (two discrete maps and one continuous flow) with theoretical results.
Chaos Generation and Synchronization Using an Integrated Source With an Air Gap
IEEE Journal of Quantum Electronics, 2000
We discuss experimentally and numerically the dynamical behavior of a novel integrated semiconductor laser subject to multiple optical feedback loops. The laser's structure consists of distributed feedback section coupled to a waveguide, an air gap section and two phase sections. It is found that the laser, due to the multiple feedback loops and under certain operating conditions, displays chaotic behaviors appropriate for chaos-based communications. The synchronization properties of two unidirectionally coupled (master-slave) systems are also studied. Finally, we find numerically the conditions for message encryption/extraction using the multiple-feedback lasers.
Realization of a digital chaotic oscillator by using a low cost microcontroller
Engineering review, 2017
This study addresses the in-detail steps to create a chaotic oscillator having continuous-time equations using a microcontroller hardware which has a lower clock-frequency and narrower data bus, as well as much lower hardware, software and algorithm development costs compared to chaotic oscillators developed using analog circuit components or a hardware-based software platform such as FPGA. For this purpose, a Lorenz chaotic oscillator with continuous-time nonlinear equations was selected. Lorenz t-domain equations were transformed into S-domain and Z-domain respectively. After these transformations, a detailed flowchart was given to illustrate the steps required to implement the chaotic oscillator in the microcontroller. All the details derived were simulated by running simultaneous MATLAB-SIMULINK simulations. And, the performance of the discrete-time chaotic oscillator executed in the PIC18F452 microcontroller produced by the Microchip Technology Inc. was visualized by 1D and 2D ...
Comparison of Chaos Synchronization and Noise Effect on Simple Oscillators
2009
In this study, the breakdown of synchronization observed from four coupled chaotic oscillators is investigated. In order to understand the phenomenon, the model of coupled modified van der Pol oscillators with chaos noise is considered. And the logistic map is used to generate chaos noise. The comparison of the coupled chaotic oscillators with the coupled modified van der Pol oscillators with chaos noise gives us some interesting results.