1,163 research outputs found
Langevin approach to synchronization of hyperchaotic time-delay dynamics
In this paper, we characterize the synchronization phenomenon of hyperchaotic
scalar non-linear delay dynamics in a fully-developed chaos regime. Our results
rely on the observation that, in that regime, the stationary statistical
properties of a class of hyperchaotic attractors can be reproduced with a
linear Langevin equation, defined by replacing the non-linear delay force by a
delta-correlated noise. Therefore, the synchronization phenomenon can be
analytically characterized by a set of coupled Langevin equations. We apply
this formalism to study anticipated synchronization dynamics subject to
external noise fluctuations as well as for characterizing the effects of
parameter mismatch in a hyperchaotic communication scheme. The same procedure
is applied to second order differential delay equations associated to
synchronization in electro-optical devices. In all cases, the departure with
respect to perfect synchronization is measured through a similarity function.
Numerical simulations in discrete maps associated to the hyperchaotic dynamics
support the formalism.Comment: 12 pages, 6 figure
Post-Double Hopf Bifurcation Dynamics and Adaptive Synchronization of a Hyperchaotic System
In this paper a four-dimensional hyperchaotic system with only one
equilibrium is considered and its double Hopf bifurcations are investigated.
The general post-bifurcation and stability analysis are carried out using the
normal form of the system obtained via the method of multiple scales. The
dynamics of the orbits predicted through the normal form comprises possible
regimes of periodic solutions, two-period tori, and three-period tori in
parameter space.
Moreover, we show how the hyperchaotic synchronization of this system can be
realized via an adaptive control scheme. Numerical simulations are included to
show the effectiveness of the designed control
Some new less conservative criteria for impulsive synchronization of a hyperchaotic Lorenz system based on small impulsive signals
In this Letter the issue of impulsive Synchronization of a hyperchaotic Lorenz system is developed. We propose an impulsive synchronization scheme of the hyperchaotic Lorenz system including chaotic systems. Some new and sufficient conditions on varying impulsive distances are established in order to guarantee the synchronizability of the systems using the synchronization method. In particular, some simple conditions are derived for synchronizing the systems by equal impulsive distances. The boundaries of the stable regions are also estimated. Simulation results show the proposed synchronization method to be effective. (C) 2009 Elsevier Ltd. All rights reserved
Multiobjective synchronization of coupled systems
Copyright @ 2011 American Institute of PhysicsSynchronization of coupled chaotic systems has been a subject of great interest and importance, in theory but also various fields of application, such as secure communication and neuroscience. Recently, based on stability theory, synchronization of coupled chaotic systems by designing appropriate coupling has been widely investigated. However, almost all the available results have been focusing on ensuring the synchronization of coupled chaotic systems with as small coupling strengths as possible. In this contribution, we study multiobjective synchronization of coupled chaotic systems by considering two objectives in parallel, i. e., minimizing optimization of coupling strength and convergence speed. The coupling form and coupling strength are optimized by an improved multiobjective evolutionary approach. The constraints on the coupling form are also investigated by formulating the problem into a multiobjective constraint problem. We find that the proposed evolutionary method can outperform conventional adaptive strategy in several respects. The results presented in this paper can be extended into nonlinear time-series analysis, synchronization of complex networks and have various applications
Using discrete-time hyperchaotic-based asymmetric encryption and decryption keys for secure signal transmission
In this paper, a framework for the synchronization of two non-identical discrete-time hyperchaotic systems, namely the 3D Baier-Klein and the 3D Hitzel-Zele maps, based on the use of hybrid output feedback concept and aggregation techniques, is employed to design a two-channel secure communication system. New sufficient conditions for synchronization are obtained by the use of Borne and Gentina practical criterion for stabilization study associated to the forced arrow form matrix for system description. The efficiency of the proposed approach to confidentially recover the transmitted message signal is shown via an application to the hyperchaotic Baier-Klein and Hitzel-Zele systems, considered as generators of asymmetric encryption and decryption keys
Phase Synchronization in Unidirectionally Coupled Ikeda Time-delay Systems
Phase synchronization in unidirectionally coupled Ikeda time-delay systems
exhibiting non-phase-coherent hyperchaotic attractors of complex topology with
highly interwoven trajectories is studied. It is shown that in this set of
coupled systems phase synchronization (PS) does exist in a range of the
coupling strength which is preceded by a transition regime (approximate PS) and
a nonsynchronous regime. However, exact generalized synchronization does not
seem to occur in the coupled Ikeda systems (for the range of parameters we have
studied) even for large coupling strength, in contrast to our earlier studies
in coupled piecewise-linear and Mackey-Glass systems
\cite{dvskml2006,dvskml2008}. The above transitions are characterized in terms
of recurrence based indices, namely generalized autocorrelation function
, correlation of probability of recurrence (CPR), joint probability of
recurrence (JPR) and similarity of probability of recurrence (SPR). The
existence of phase synchronization is also further confirmed by typical
transitions in the Lyapunov exponents of the coupled Ikeda time-delay systems
and also using the concept of localized sets.Comment: 10 pages, 7 figure
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