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.