Maximum Condition Lyapunov Exponent Research Articles

Multivalued synchronization by Poincaré coupling

This work presents multivalued chaotic synchronization via coupling based on the Poincaré plane. The coupling is carried out by an underdamped signal, triggered every crossing event of the trajectory of the master system through a previously defined Poincaré plane. A master–slave system is explored, and the synchronization between the systems is detected via the auxiliary system approach and the maximum conditional Lyapunov exponent. Due to the response to specific conditions two phenomena may be obtained: univalued and multivalued synchronization. Since the Lyapunov exponent is not enough to detect these two phenomena, the distance between the pieces of trajectories of the slave and auxiliary systems with different initial conditions is also used as a tool for the detection of multivalued synchronization. Computer simulations using the benchmark chaotic systems of Lorenz and Rössler are used to exemplify the approach proposed.

GENERALIZED SYNCHRONIZATION OF CHAOS IN RCL-SHUNTED JOSEPHSON JUNCTIONS BY UNIDIRECTIONALLY COUPLING

This paper investigates chaotic synchronization in the generalized sense in two resistive-capacitive-inductive-shunted (RCL-shunted) Josephson junctions (RCLSJJs) by using the means of unidirectionally coupling. The numerical simulations confirm that the generalized synchronization of chaos in these two systems can be achieved with a suitable coupling intensity when the maximum condition Lyapunov exponent (MCLE) is negative. Also, the auxiliary system approach is used to detect the existence of the generalized synchronization.

Synchronization of chaos in resistive-capacitive-inductive shunted Josephson junctions

We present a scheme for chaotic synchronization in two resistive- capacitive-inductive shunted Josephson junctions (RCLSJJs) by using another chaotic RCLSJJ as a driving system. Numerical simulations show that whether the two RCLSJJs are chaotic or not before being driven, they can realize chaotic synchronization with a suitable driving intensity, under which the maximum condition Lyapunov exponent (MCLE) is negative. On the other hand, if the driving system is in different periodic states or chaotic states, the two driven RCLSJJs can be controlled into the periodic states with different period numbers or chaotic states but still maintain the synchronization.

Chaos synchronization in RCL-shunted Josephson junctions via a common chaos driving

We study chaos synchronization in two resistive-capacitive-inductive-shunted (RCL-shunted) Josephson junctions (RCLSJJs) by using a common chaos driving. The numerical simulations confirm that the synchronization of two RCLSJJs can be achieved with a suitable driving intensity when the maximum condition Lyapunov exponent (MCLE) is negative.

A new method for line spectra reduction similar to generalized synchronization of chaos

Line spectra in the radiated noise of marine vessels are the most visible signs, which can be detected, tracked and identified by enemy's passive sonar, and hence it is of great significance to reduce the line spectra for improving the acoustic stealth of marine vessels. In this paper, a driving parameter scheme using an external chaotic signal to drive a nonlinear vibration isolation system (VIS) of onboard machinery is presented to make the chaotic motion in the nonlinear VIS persistent, which is similar to generalized synchronization of chaos in some sense. In this way, the line spectra in the radiated noise can be reduced effectively because the response spectrum of a chaotic system under harmonic excitations is a continuous and reduced one. Numerical simulations are carried out and the results confirm the effectiveness of this method. The maximum conditional Lyapunov exponent is calculated numerically and its negative value indicates the stability of this driving parameter control scheme.

Chaotic synchronization of nearest-neighbor diffusive coupling Hindmarsh–Rose neural networks in noisy environments

The chaotic synchronization of Hindmarsh–Rose neural networks linked by a nonlinear coupling function is discussed. The HR neural networks with nearest-neighbor diffusive coupling form are treated as numerical examples. By the construction of a special nonlinear-coupled term, the chaotic system is coupled symmetrically. For three and four neurons network, a certain region of coupling strength corresponding to full synchronization is given, and the effect of network structure and noise position are analyzed. For five and more neurons network, the full synchronization is very difficult to realize. All the results have been proved by the calculation of the maximum conditional Lyapunov exponent.

Phase synchronization and anti-phase synchronization of chaos for degenerate optical parametric oscillator

We have investigated chaotic synchronization in the generalized sense for the degenerate optical parametric oscillator (DOPO). The numerical results show that two unidirectional coupling DOPOs in chaos can be completely phase synchronization or anti-phase synchronization with a suitable coupling coefficient under which the maximum condition Lyapunov exponent (MCLE) is negative. Phase synchronization and anti-phase synchronization of chaos can be realized through positive and negative coupling. On the other hand, the different synchronization states depend on the coupling types used in the DOPO systems.

Generalized synchronization of chaos in erbium-doped dual-ring lasers

We investigate chaotic synchronization in the generalized sense in unidirectionally coupled erbium-doped fibre dual-ring lasers. Numerical simulation shows that no matter whether the two different erbium-doped fibre dual-ring lasers are chaotic or not before coupling, they show generalized synchronization with a suitable unidirectional coupling coefficient under which the maximum condition Lyapunov exponent is negative. We also use the auxiliary system approach to detect the generalized synchronization.

SELF CONTROL FEEDBACK SYNCHRONIZATION OF CHAOS BYCOUPLING-DRIVING IN ACOUSTO-OPTIC BISTABLE SYSTEM

The paper proposes theoretically the method of chaos synchronization by self-controlled feedback coupling-driving,and studies numerically on the condition of chaotic synchronization in two Bragg acousto-optic bistable (AOB) systems. The maximum conditional Lyapunov exponent (MCLE) are considered as the criteria of synchronization. It is found that one can gain the chaotic outputs synchronized of the two systems if one system is coupling-driven appropriately by another. When self-controlled feedback on parameter introduced, synchronization can be realized faster and the required minimum stiffness of coupling is decreased. The synchronization is also gained when the effect of noise is considered. The result of experimental test is also given.