On the mathematical clarification of the snap-back-repeller in high-dimensional systems and chaos in a discrete neural network model
文献类型：期刊论文
| 作者 | Lin, W; Ruan, J; Zhao, WR |
| 刊名 | INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
 |
| 出版日期 | 2002-05-01 |
| 卷号 | 12期号:5页码:1129-1139 |
| 关键词 | snap-back-repeller chaos discrete neural networks |
| ISSN号 | 0218-1274 |
| 英文摘要 | 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 I 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. |
| WOS研究方向 | Mathematics ; Science & Technology - Other Topics |
| 语种 | 英语 |
| WOS记录号 | WOS:000176713500018 |
| 出版者 | WORLD SCIENTIFIC PUBL CO PTE LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/17163]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Ruan, J |
| 作者单位 | 1.Fudan Univ, Res Ctr, Dept Math, Shanghai 200433, Peoples R China 2.Fudan Univ, Lab Math Nonlinear Sci, Dept Math, Shanghai 200433, Peoples R China 3.Fudan Univ, Lab Math Nonlinear Sci, Math Inst, Shanghai 200433, Peoples R China 4.Fudan Univ, Res Ctr, Math Inst, Shanghai 200433, Peoples R China |
| 推荐引用方式 GB/T 7714 | Lin, W,Ruan, J,Zhao, WR. On the mathematical clarification of the snap-back-repeller in high-dimensional systems and chaos in a discrete neural network model[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS,2002,12(5):1129-1139. |
| APA | Lin, W,Ruan, J,&Zhao, WR.(2002).On the mathematical clarification of the snap-back-repeller in high-dimensional systems and chaos in a discrete neural network model.INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS,12(5),1129-1139. |
| MLA | Lin, W,et al."On the mathematical clarification of the snap-back-repeller in high-dimensional systems and chaos in a discrete neural network model".INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 12.5(2002):1129-1139. |
入库方式： OAI收割
来源：数学与系统科学研究院
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