Global Robust Stability Criteria for Interval Delayed Full-Range Cellular Neural Networks

Discontinuous Neural Networks for Finite-Time Solution of Time-Dependent Linear Equations

This paper considers a class of nonsmooth neural networks with discontinuous hard-limiter (signum) neuron activations for solving time-dependent (TD) systems of algebraic linear equations (ALEs). The networks are defined by the subdifferential with respect to the state variables of an energy function given by the L ₁ norm of the error between the state and the TD-ALE solution. It is shown that when the penalty parameter exceeds a quantitatively estimated threshold the networks are able to reach in finite time, and exactly track thereafter, the target solution of the TD-ALE. Furthermore, this paper discusses the tightness of the estimated threshold and also points out key differences in the role played by this threshold with respect to networks for solving time-invariant ALEs. It is also shown that these convergence results are robust with respect to small perturbations of the neuron interconnection matrices. The dynamics of the proposed networks are rigorously studied by using tools from nonsmooth analysis, the concept of subdifferential of convex functions, and that of solutions in the sense of Filippov of dynamical systems with discontinuous nonlinearities.

Theorems and application of local activity of CNN with five state variables and one port

Coupled nonlinear dynamical systems have been widely studied recently. However, the dynamical properties of these systems are difficult to deal with. The local activity of cellular neural network (CNN) has provided a powerful tool for studying the emergence of complex patterns in a homogeneous lattice, which is composed of coupled cells. In this paper, the analytical criteria for the local activity in reaction-diffusion CNN with five state variables and one port are presented, which consists of four theorems, including a serial of inequalities involving CNN parameters. These theorems can be used for calculating the bifurcation diagram to determine or analyze the emergence of complex dynamic patterns, such as chaos. As a case study, a reaction-diffusion CNN of hepatitis B Virus (HBV) mutation-selection model is analyzed and simulated, the bifurcation diagram is calculated. Using the diagram, numerical simulations of this CNN model provide reasonable explanations of complex mutant phenomena during therapy. Therefore, it is demonstrated that the local activity of CNN provides a practical tool for the complex dynamics study of some coupled nonlinear systems.

Multistability of neural networks with time-varying delays and concave-convex characteristics

In this paper, stability of multiple equilibria of neural networks with time-varying delays and concave-convex characteristics is formulated and studied. Some sufficient conditions are obtained to ensure that an n-neuron neural network with concave-convex characteristics can have a fixed point located in the appointed region. By means of an appropriate partition of the n-dimensional state space, when nonlinear activation functions of an n-neuron neural network are concave or convex in 2k+2m-1 intervals, this neural network can have (2k+2m-1)n equilibrium points. This result can be applied to the multiobjective optimal control and associative memory. In particular, several succinct criteria are given to ascertain multistability of cellular neural networks. These stability conditions are the improvement and extension of the existing stability results in the literature. A numerical example is given to illustrate the theoretical findings via computer simulations.