时滞耦合惯性项神经系统的多混沌路径共存

李小虎; 张定一; 宋自根

doi:10.21656/1000-0887.400130

时滞耦合惯性项神经系统的多混沌路径共存

doi: 10.21656/1000-0887.400130

¹上海海洋大学信息学院, 上海 201306;²上海海洋大学食品学院, 上海 201306

基金项目: 国家自然科学基金（11672177）

详细信息

作者简介:
李小虎（1999—），男（E-mail: lixiaohusha@qq.com）;宋自根（1979—），男，副教授（通讯作者. E-mail: zigensong@163.com）.

中图分类号: O175
计量
- 文章访问数: 1268
- HTML全文浏览量: 189
- PDF下载量: 281
- 被引次数: 0
出版历程
- 收稿日期: 2019-04-01
- 修回日期: 2019-10-18
- 刊出日期: 2020-06-01

Multistage Coexistence of Different Chaotic Routes in a Delayed Neural System

¹College of Information Technology, Shanghai Ocean University, Shanghai 201306, P.R.China;²College of Food Sciences and Technology, Shanghai Ocean University, Shanghai 201306, P.R.China

Funds: The National Natural Science Foundation of China（11672177）

摘要

摘要: 混沌及其共存是神经动力学的一个重要研究内容.该文基于非单调激活函数的惯性项神经元时滞耦合系统，在固定系统参数的情况下，以耦合时滞τ作为参变量，取不同的初始条件，利用Poincaré截面技术，展现了系统多个不同的倍周期分岔序列和概周期分岔序列，并给出了系统相应的相图.研究结果表明，时滞耦合神经系统具有多级倍周期分岔序列和概周期分岔序列的稳态共存，展现了系统更加丰富的多混沌和多周期解的多稳态共存.
- 神经系统 /
- 时滞 /
- 倍周期分岔 /
- 概周期分岔 /
- 共存 /
- 混沌路径
Abstract: Chaos and its coexistence involve very important problems in dynamical analysis. A delayed inertial 2-neuron system with non-monotonic activation function was studied with the Poincaré section method. With system parameters fixed and time delay τ chosen as the parametric variable, 1D bifurcation diagrams, i. e. period-doubling and quasi-periodic bifurcations were given under different initial conditions. The results show that, the neural system exhibits multistage coexistence of many period-doubling and quasi-periodic bifurcation sequences along different routes to chaos and stable coexistence of many chaotic attractors and multi-periodic solutions.
- neural system /
- time delay /
- period-doubling bifurcation /
- quasi-periodic bifurcation /
- coexistence /
- chaos route

HTML全文

参考文献(19)

[1]	PISARCHIK A N, FEUDEL U. Control of multistability[J]. Physics Reports,2014,540(4): 167-218.
[2]	AIHARA K, TAKABE T, TOYODA M. Chaotic neural networks[J]. Physics Letter A,1990,144(67): 333-340.
[3]	HUANG W Z, HUANG Y. Chaos, bifurcation and robustness of a class of Hopfield neural networks[J]. International Journal of Bifurcation and Chaos,2011,21(3): 885-895.
[4]	CHEN P F, CHEN Z Q, WU W J. A novel chaotic system with one source and two saddle-foci in Hopfield neural networks[J]. Chinese Physics B,2010,4: 134-139.
[5]	PISARCHIK A N, JAIMES-REATEGUI R, GARCA-VELLISCA M A. Asymmetry in electrical coupling between neurons alters multistable firing behavior[J]. Chaos,2018,28(3): 033605.
[6]	CHENG C Y. Coexistence of multistability and chaos in a ring of discrete neural network with delays[J]. International Journal of Bifurcation and Chaos,2010,20(4): 1119-1136.
[7]	SONG Z G, XU J, ZHEN B. Multitype activity coexistence in an inertial two-neuron system with multiple delays[J]. International Journal of Bifurcation and Chaos,2015,25(13): 1530040.
[8]	LAI Q, HUANG J N. Coexistence of multiple attractors in a new chaotic system[J]. Acta Physica Polonica B: Particle Physics & Field,2016,47(10): 2315-2323.
[9]	JIMENEZ-LOPEZ E, GONZALEZ SALAS J S, ONTANON-GARCIA L J, et al. Generalized multistable structure via chaotic synchronization and preservation of scrolls[J]. Journal of the Franklin Institute,2013,350(10): 2853-2866.
[10]	MAURO A, CONTI F, DODGE F, et al. Subthreshold behavior and phenomenological impedance of the squid giant axon[J]. The Journal of General Physiology,1970,55: 497-523.
[11]	ANGELAKI D E, CORREIA M J. Models of membrane resonance in pigeon semicircular canal type Ⅱ hair cells[J]. Biological Cybernetics,1991,〖STHZ〗 65(1): 1-10.
[12]	TANI J. Proposal of chaotic steepest descent method for neural networks and analysis of their dynamics[J]. Electronics and Communications in Japan (Part 3: Fundamental Electronic Science),1992,75(4): 62-70.
[13]	BABCOCK K L, WESTERVELT R M. Dynamics of simple electronic neural networks[J]. Physica D,1987,28: 305-316.〖JP〗
[14]	SONG Z G, XU J. Stability switches and Bogdanov-Takens bifurcation in an inertial two-neuron coupling system with multiple delays[J]. Science China Technological Sciences,2014,57: 893-904.
[15]	SONG Z G, WANG C H, ZHEN B. Codimension-two bifurcation and multistability coexistence in an inertial two-neuron system with multiple delays[J]. Nonlinear Dynamics,2016,85: 2099-2113.
[16]	YAO S W, DING L W, SONG Z G, et al. Two bifurcation routes to multiple chaotic coexistence in an inertial two-neural system with time delay[J]. Nonlinear Dynamics,2019,〖STHZ〗 95: 1-15.
[17]	CRESPI B. Storage capacity of non-monotonic neurons[J]. Neural Networks,1999,12(10): 1377-1389.
[18]	LI C G, CHEN G R. Coexisting chaotic attractors in a single neuron model with adapting feedback synapse[J]. Chaos, Solitons & Fractals,2005,23: 1599-1604.
[19]	LI Chunguang, CHEN Guangrong, LIAO Xiaofeng, et al. Hopf bifurcation and chaos in a single inertial neuron model with time delay[J]. The European Physical Journal B:Condensed Matter and Complex Systems,2004,41: 337-343.