Stability and Bifurcation Analysis of a Class of Networked Dynamical Systems

Abstract

In this brief, stability and bifurcation in a class of networked dynamical systems are investigated. First, it is shown that, for each member of the family, there is a globally attracting region. Then, the local stability of a particular fixed point (0, 0) is investigated; afterward, it is found that this fixed point is a bifurcation point as a certain system parameter varies. Finally, a family of 3-D dynamical systems is numerically studied, with rich and diverse bifurcating phenomena and geometrically different attractors being revealed. It is also observed that the geometry of attractors undergoes continuous deformation as a function of a certain parameter.

Convergence Theory for Unified Discrete-Time RNNs with Quasi-Symmetric Connection

“…The theorem removed the restrains that W must be the symmetric matrix [1]. From the convergent conditions above, it is clear that the theory here contains the global convergence theory in [1][2][3][4][5][6].…”

“…For the important value of application of the recurrent neural network, lots of RNN models have been developed recently [1][2][3][4][5][6]. It is worthy to pointing out that the different model forms result no directly lateral comparability between different models and their performances.…”