A note on neural networks with multiple equilibrium points

Author(s):  
M. Forti
2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yanke Du ◽  
Yanlu Li ◽  
Rui Xu

A general class of Cohen-Grossberg neural networks with time-varying delays, distributed delays, and discontinuous activation functions is investigated. By partitioning the state space, employing analysis approach and Cauchy convergence principle, sufficient conditions are established for the existence and locally exponential stability of multiple equilibrium points and periodic orbits, which ensure thatn-dimensional Cohen-Grossberg neural networks withk-level discontinuous activation functions can haveknequilibrium points orknperiodic orbits. Finally, several examples are given to illustrate the feasibility of the obtained results.


2009 ◽  
Vol 21 (5) ◽  
pp. 1434-1458 ◽  
Author(s):  
Xuemei Li

This letter discusses the complete stability of discrete-time cellular neural networks with piecewise linear output functions. Under the assumption of certain symmetry on the feedback matrix, a sufficient condition of complete stability is derived by finite trajectory length. Because the symmetric conditions are not robust, the complete stability of networks may be lost under sufficiently small perturbations. The robust conditions of complete stability are also given for discrete-time cellular neural networks with multiple equilibrium points and a unique equilibrium point. These complete stability results are robust and available.


2019 ◽  
Vol 30 (12) ◽  
pp. 2050004
Author(s):  
Ning Cui ◽  
Junhong Li

This paper formulates a new hyperchaotic system for particle motion. The continuous dependence on initial conditions of the system’s solution and the equilibrium stability, bifurcation, energy function of the system are analyzed. The hyperchaotic behaviors in the motion of the particle on a horizontal smooth plane are also investigated. It shows that the rich dynamic behaviors of the system, including the degenerate Hopf bifurcations and nondegenerate Hopf bifurcations at multiple equilibrium points, the irregular variation of Hamiltonian energy, and the hyperchaotic attractors. These results generalize and improve some known results about the particle motion system. Furthermore, the constraint of hyperchaos control is obtained by applying Lagrange’s method and the constraint change the system from a hyperchaotic state to asymptotically state. The numerical simulations are carried out to verify theoretical analyses and to exhibit the rich hyperchaotic behaviors.


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