Integro-differential inequality and stability of BAM FCNNs with time delays in the leakage terms and distributed delays

Abstract

In this paper, a class of impulsive bidirectional associative memory (BAM) fuzzy cellular neural networks (FCNNs) with time delays in the leakage terms and distributed delays is formulated and investigated. By establishing an integro-differential inequality with impulsive initial conditions and employing M-matrix theory, some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive BAM FCNNs with time delays in the leakage terms and distributed delays are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on the delay kernel functions and system parameters. It is believed that these results are significant and useful for the design and applications of BAM FCNNs. An example is given to show the effectiveness of the results obtained here.

Existence of Exponentialp-Stability Nonconstant Equilibrium of Markovian Jumping Nonlinear Diffusion Equations via Ekeland Variational Principle

“…In this paper, we also need to consider the equilibrium solution of (4) defined on [ 0 , +∞). Different from [22,23], we consider the nonconstant equilibrium solution = * ( ) = ( * 1 ( ), * 2 ( ), . .…”

“…Motivated by [27], we proposed some conditions on activation functions to set up existence criterion for the equilibrium solution of system (4). In [22,23], the constant equilibrium solution = * for all ∈ [ 0 , +∞) was obtained by homomorphic mapping theory and matrix theory, or matrix theory and homotopy invariance theorem, where * = ( * 1 , * 2 , . .…”

“…Our methods employed in this paper are different from those of previous related literature. For example, homomorphic mapping theory was employed to obtain the existence of equilibrium of ordinary differential equations in [22]; topological degree theory was used to obtain the existence of equilibrium for fuzzy ordinary differential equations in [23] and of equilibrium for reaction-diffusion partial differential equations in [17]. In this paper, Ekeland variational principle is originally proposed to solve the existence of nonconstant equilibrium for nonlinear diffusion equations.…”