The multifractal dimension of chaotic attractors has been studied in a weakly coupled superlattice driven by an incommensurate sinusoidal voltage as a function of the driving voltage amplitude. The derived multifractal dimension for the observed bifurcation sequence shows different characteristics for chaotic, quasiperiodic, and frequency-locked attractors. In the chaotic regime, strange attrac...

The chaotic neural network constructed with chaotic neuron shows the associative memory function, but its memory searching process cannot be stabilized in a stored state because of the chaotic motion of the network. In this paper, a pinning control method focused on the chaotic neural network is proposed. The computer simulation proves that the chaos in the chaotic neural network can be control...

This paper concerns global phase structures of a time-delayed-feedback controlled two-well Duffing system. The remains of a global stretch and fold structure along an unstable manifold, which develops from an unstable fixed point in function space, reveals that the global chaotic dynamics is inherited from the original system by the controlled system. The remains of the original chaotic dynamic...

In this paper, the dynamical behavior of a new chaotic system is discussed, the globally exponentially attractive set and positive invariant set of the chaotic systems are studied via the generalized Lyapunov function, the result is applied to the study of chaos synchronization, and the globally exponential synchronization of the chaotic system is achieved. Numerical simulation results are pres...

In this paper, we derive new results for backstepping controller design for the anti-synchronization of Arneodo chaotic system (1980). Backstepping control is a recursive procedure that combines the choice of a Lyapunov function with the design of a feedback controller. In anti-synchronization of chaotic systems, the states of the synchronized systems have the same absolute values, but opposite...

We introduce in this paper a new chaotic map with dynamical properties controlled by two free parameters. The map definition is based on the hyperbolic tangent function, so it is called the tanh map. We demonstrate that the Lyapunov exponent of the tanh map is robust, remaining practically unaltered with the variation of its parameters. As the main application, we consider a chaotic communicati...

Based on the Lyapunov stabilization theory and Gerschgorin theorem, a simple generic criterion is derived for global synchronization of two coupled chaotic systems with a unidirectional linear error feedback coupling. This simple criterion is applicable to a large class of chaotic systems, where only a few algebraic inequalities are involved. To demonstrate the efficiency of design, the suggest...

Recent work has considered the possibility of utilizing symbolic representations of controlled chaotic orbits for digital communication. We argue that dynamically a coding scheme usually leads to trajectories that live on a nonattracting but noise-resisting chaotic saddle embedded in the chaotic attractor. We present analyses and numerical computation which indicate that the channel capacity of...

In the present work, the chaotic motion control of a mobile robot is studied, in order to cover a terrain with unpredictable way. The proposed control strategy is based on a chaotic path planning generator. As a chaotic generator, we have used three different nonlinear dynamical systems, the Chua oscillator, the Lorenz system, and a nonlinear circuit with a nonlinear resistor having an i-v char...

In this paper, a magnetron memristor model based on hyperbolic sine function is presented and the correctness proved by studying the trajectory of its voltage and current phase, and then a memristor chaotic system with the memristor model is presented. The phase trajectories and the bifurcation diagrams and Lyapunov exponent spectrum of the magnetron memristor system are plotted by numerical si...