A new 4D fractional-order chaotic system, which has an infinite number of equilibrium points, is introduced. There is no-chaotic behavior for its corresponded integer-order system. We obtain that the largest Lyapunov exponent of this 4D fractional-order chaotic system is 0.8939 and yield the chaotic attractor. A chaotic synchronization scheme is presented for this 4D fractional-order chaotic sy...

Interior crises are understood as discontinuous changes of the size of a chaotic attractor that occur when an unstable periodic orbit collides with the chaotic attractor. We present here numerical evidence and theoretical reasoning which prove the existence of a chaos-chaos transition in which the change of the attractor size is sudden but continuous. This occurs in the Hindmarsh-Rose model of ...

In this letter we unveil the existence of transient hidden coexisting chaotic attractors, in a simplified Hopfield neural network with three neurons. keyword Hopfield neural network; Transient hidden chaotic attractor; Limit cycle

In this note we construct strange attractors in a class of skew product dynamical systems. A dynamical system of the class is a bundle map of a trivial bundle whose base is a compact metric space and the fiber is the non-negative half real line. The map on the base is a homeomorphism preserving an ergodic measure. The fiber maps either are strictly monotone and strictly concave or collapse at z...

<p style='text-indent:20px;'>Based on the method of compression and pull forming mechanism (CAP), authors in a well-known paper proposed analyzed Lü-like system: <inline-formula><tex-math id="M1">\begin{document}$ \dot{x} = a(y - x) + dxz $\end{document}</tex-math></inline-formula>, id="M2">\begin{document}$ \dot{y} xz fy id="M3">\begin{document}$ \dot{z} -ex...

Based on Lyapunov stability theory and matrix measure, this paper presents a new generic criterion of global chaotic synchronization for bidirectional coupled chaotic system with time-delay. A new chaotic system with four-scroll attractor is chosen as an example to verify the effectiveness of the criterion. Numerical simulation are shown for demonstration. 2006 Published by Elsevier Ltd.

A dynamic antigen response of the immune network is discussed, based on shape-space modelling. The present model extends the shape-space modelling by introducing the evolution of speci"city of idiotypes. When the amount of external antigen increases, a measure of stability of the immune network is lost and thus the network can respond to the antigen. It is shown that speci"c and non-speci"c res...