Affiliation:
1. Research Center and Laboratory of Mathematics for Nonlinear Science, Department and Institute of Mathematics, Fudan University, Shanghai 200433, P. R. China
Abstract
We investigate the differences among several definitions of the snap-back-repeller, which is always regarded as an inducement to produce chaos in nonlinear dynamical system. By analyzing the norms in different senses and the illustrative examples, we clarify why a snap-back-repeller in the neighborhood of the fixed point, where all eigenvalues of the corresponding variable Jacobian Matrix are absolutely larger than 1 in norm, might not imply chaos. Furthermore, we theoretically prove the existence of chaos in a discrete neural networks model in the sense of Marotto with some parameters of the systems entering some regions. And the following numerical simulations and corresponding calculation, as concrete examples, reinforce our theoretical proof.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)
Reference28 articles.
1. Snap-back repellers and scrambled sets in general topological spaces
2. Snapback repellers as a cause of chaotic vibration of the wave equation with a van der Pol boundary condition and energy injection at the middle of the span
3. L. Chen and K. Aihara, Transient Chaotic Neural Networks and Chaotic Simulated Annealing, Towards the Harnessing of Chaos, ed. M. Yamaguti (Elsevier, Amsterdam, 1994) pp. 347–352.
4. Chaotic simulated annealing by a neural network model with transient chaos
5. L. Chen and K. Aihara, Chaotic Simulated Annealing for Combinatorial Optimization, Dynamic Systems and Chaos 1, eds. Aoki (World Scientific, Singapore, 1995) pp. 319–322.
Cited by
26 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献