Effects of Low and High Neuron Activation Gradients on the Dynamics of a Simple 3D Hopfield Neural Network

被引:25
作者
Isaac, Sami Doubla [1 ,2 ]
Njitacke, Z. Tabekoueng [3 ]
Kengne, J. [1 ]
机构
[1] Univ Dschang, Dept Elect Engn, IUT PV Bandjoun, Unite Rech Automat & Informat Appl URAIA, Dschang, Cameroon
[2] Univ Dschang, Dept Phys, Unite Rech Matiere Condensee Elect & Traitement S, POB 67, Dschang, Cameroon
[3] Univ Buea, Dept Elect & Elect Engn, Coll Technol COT, POB 63, Buea, Cameroon
来源
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2020年 / 30卷 / 11期
关键词
Hopfield neuronal network (HNN); activation gradient; electrical activity; multistability; PSpice simulation; COEXISTING MULTIPLE ATTRACTORS; SMOOTHLY ADJUSTABLE SYMMETRY; NUMERICAL-ANALYSES; JERK SYSTEM; NONLINEARITY CHAOS; STRANGE ATTRACTORS; COMPLEX DYNAMICS; HYPERCHAOS; CIRCUIT; MODEL;
D O I
10.1142/S021812742050159X
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, the effects of low and fast response speeds of neuron activation gradient of a simple 3D Hopfield neural network are explored. It consists of analyzing the effects of low and high neuron activation gradients on the dynamics. By considering an imbalance of the neuron activation gradients, different electrical activities are induced in the network, which enable the occurrence of several nonlinear behaviors. The significant sensitivity of nontrivial equilibrium points to the activation gradients of the first and second neurons relative to that of the third neuron is reported. The dynamical analysis of the model is done in a wide range of the activation gradient of the second neuron. In this range, the model presents areas of periodic behavior, chaotic behavior and periodic window behavior through complex bifurcations. Interesting behaviors such as the coexistences of two, four, six and eight disconnected attractors, as well as the phenomenon of coexisting antimonotonicity, are reported. These singular results are obtained by using nonlinear dynamics analysis tools such as bifurcation diagrams and largest Lyapunov exponents, phase portraits, power spectra and basins of attraction. Finally, some analog results obtained from PSpice-based simulations further verify the numerical results.
引用
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页数:26
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