Results 1 - 10 of 82
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[en] In this paper a proposal is made of an adaptive coupling function for achieving synchronization between two lasers subject to optical feedback. Such a control scheme requires knowledge of the systems' parameters. For the first time we demonstrate that when these parameters are not available on-line parameter estimation can be applied. Generalization of the approach to the multi-feedback systems is also presented. (author)
[en] This paper investigates the fundamental dynamical mechanism responsible for transition to chaos in periodically modulated Duffing-Van der Pol oscillator. It is shown that a modulationally unstable pattern appears into an initially stable motionless state. A further spatiotemporal transition occurs with a sharp interface from the selected stable pattern to a stabilized pattern or chaotic state. Also, the synchronization of the chaotic state of the model is investigated. The results are discussed in the context of generalized synchronization. The main idea is to construct an augmented dynamical system from the synchronization error system, which is itself uncertain. The advantage of this method over existing results is that the synchronization time is explicitly computed. Numerical simulations are provided to verify the operation of the proposed algorithm. (author)
[en] In recent years, the study of synchronization of identical chaotic systems subjected to a common fluctuating random driving signal has drawn considerable interest. In this communication, we report that it is possible to achieve synchronization between two identical chaotic systems, which are not coupled directly but subjected to an external chaotic signal. The external chaotic signal may be obtained from any chaotic system identical or non-identical to both identical chaotic systems. Results of numerical simulations on well known Roessler and jerk dynamical systems have been presented. (author)
[en] We consider in this paper the dynamics and synchronization of coupled chaotic Van der Pol-Duffing systems. The stability of the synchronization process between two coupled autonomous Van der Pol model is first analyzed analytically and numerically, before following the problem of synchronizing chaos both on the same and different chaotic orbits of two coupled Van der Pol-Duffing systems. The stability boundaries of the synchronization process are derived and the effects of the amplitude of the periodic perturbation of the coupling parameter on these boundaries are analyzed. The results are provided on the stability map in the (q, K) plane. (author)
[en] We report on inverse chaos synchronization between two unidirectionally linearly and nonlinearly coupled chaotic systems with multiple time-delays and find the existence and stability conditions for different synchronization regimes. We also study the effect of parameter mismatches on synchonization regimes. The method is tested on the famous Ikeda model. Numerical simulations fully support the analytical approach. (author)
[en] Physics of chaos in a localized phase-space region is exploited to produce a longitudinally uniformly distributed beam. Theoretical study and simulations are used to study its origin and applicability in phase-space dilution of beam bunch. Through phase modulation to a double-rf system, a central region of localized chaos bounded by invariant tori are generated by overlapping parametric resonances. Condition and stability of the chaos will be analyzed. Applications include high-power beam, beam distribution uniformization, and industrial beam irradiation.
[en] We discuss the general structure and observational consequences of some of the simplest versions of chaotic inflation in supergravity in relation to the data by Planck 2013 and BICEP2. We show that minimal modifications to the simplest quadratic potential are sufficient to provide a controllable tensor mode signal and a suppression of CMB power at large angular scales.
[en] We investigate synchronization between two undirectionally linearly coupled chaotic nonidentical time-delayed systems and show that parameter mismatches are of crucial importance to achieve synchronization. We establish that independent of the relation between the delay time in the coupled systems and the coupling delay time, only retarded synchronization with the coupling delay time is obtained. We show that with parameter mismatch or without it neither complete nor anticipating synchronization occurs. We derive existence and stability conditions for the retarded synchronization manifold. We demonstrate our approach using examples of the Ikeda and Mackey Glass models. Also for the first time we investigate chaos synchronization in time-delayed systems with variable delay time and find both existence and sufficient stability conditions for the retarded synchronization manifold with the coupling-delay lag time. (author)
[en] In this paper the exponential control problem for a class of chaotic systems with affine dependence on the control is addressed and solved by the controllability approach. It is shown that the controllability approach in conjunction with Lyapunov Direct Method yields a promising way of controlling chaotic dynamics. The proposed strategy is an input-output control scheme which comprises a state estimator and an exponential linearizing feedback. The proposed output feedback controller allows chaos suppression and can be applied to a large class of chaotic systems. Explicit expression of the control time is given. Computer simulations confirm the feasibility of the proposed approach. (author)