In this work, we study chaos control and synchronization of the commensurate fractional order Liu system. Based on the stability theory of fractional order systems, the conditions of local stability of nonlinear three-dimensional commensurate fractional order systems are discussed. The existence and uniqueness of solutions for a class of commensurate fractional order Liu systems are investigate...

This work presents an application of the previously proposed Support Vector Machines Based Generalized Predictive Control (SVM-Based GPC) method [1] to the problem of controlling chaotic dynamics with small parameter perturbations. The Generalized Predictive Control (GPC) method, which is included in the class of Model Predictive Control, necessitates an accurate model of the plant that plays v...

Information networks are an important infrastructure and their resources are shared by many users. In order to utilize their resources efficiently, they should be controlled to prevent synchronization of user traffic. In addition, fairness among users must be assured. This paper discusses the framework of transmission rate control based on chaos. There are two different characteristics that coe...

Chaos is a special feature of complex parametric nonlinear dynamical systems. It has the random-like behavior usually seen in stochastic systems although it is associated with deterministic dynamics. Chaos is at the edge of stability and therefore could easily lead systems to an unstable, performance-degraded, or even catastrophic situation. In such cases, chaos is considered as undesired and s...

We report on an experimental observation of optical wave chaos in a resonator consisting of three standard, high-reflectivity mirrors. The nonseparability of the wave equation necessary for chaos is introduced by violating the paraxial approximation. Until recently progress in optical wave chaos was hampered by the inherent difficulty in realizing suitable microscopic systems; now this novel, m...

This paper surveys frequency-domain and time-domain methods for feedback nonlinear systems and their possible applications to chaos control, coupled systems and complex dynamical networks. The absolute stability of Lur’e systems with single equilibrium and global properties of a class of pendulum-like systems with multi-equilibria are discussed. Time-domain and frequency-domain criteria for the...

We carried out a fluid dynamical simulation for a forced dripping faucet system using a new algorithm that was recently developed. The simulation shows that periodic external forcing induces transitions from chaotic to periodic motion and vice versa. We further constructed an improved mass-sprig model for the same system on the basis of data obtained from the fluid dynamical computations. A det...

This paper surveys some recent results about chaos induced by snap-back repellers and its applications to anti-control of chaos (or, chaotification). Several criteria of chaos induced by snap-back repellers in finite and infinite dimensional dynamical systems are introduced. Some successful applications are given to chaotification problems for finite and infinitedimensional discrete dynamical s...

This paper presents anti-synchronization of two different chaotic systems using optimal control method. The proposed technique is applied to achieve chaos anti-synchronization for the new fourdimensional and hyperchaotic Lü systems with fully unknown parameters. Numerical simulations results are presented to demonstrate the effectiveness of the method.