Attraction/repulsion functions in a new class of chaotic systems

In this Letter, a new kind of chaotic system is introduced by combining a three-dimensional linear system with attraction/repulsion functions developed in the context of swarm aggregations. Rich chaotic oscillating phenomena appear in this new system. Some simple extension to multi-input and multi-output systems is also given. The frequency-domain condition for the property of dichotomy is presented for a more general system. Based on the frequency-domain condition given here, some parameter domains can be determined for the nonexistence of chaotic attractors or limit cycles in the system given in this Letter. (C) 2004 Elsevier B.V. All rights reserved.