Stochastic stability criteria with LMI conditions for Markovian jumping impulsive BAM neural networks with mode-dependent time-varying delays and nonlinear reaction–diffusion

• The first stability criterion of p-Laplace diffusion neural networks is obtained.
• The new criteria admit less conservatism and higher computational efficiency.
• The new criteria are more general than some existing results.
• And the numerical example verifies the effectiveness.

In this paper, the problem of stochastic stability for Markovian jumping impulsive BAM neural networks with mode-dependent time-varying delays and nonlinear diffusion has been investigated. The non-linear p  -Laplace diffusion gives a great difficulty in playing its role about judging the stability of stochastic system. By employing the Lyapunov technique, the linear matrix inequality (LMI) approach and variational methods in Sobolev space W1,p(Ω)W1,p(Ω), a series of new criteria are obtained. The new criteria have advantages over some previous ones due to less conservatism and higher computational efficiency. Besides, since linear Laplace reaction–diffusion is only the special example of p  -Laplacian (in the case of p=2p=2), the new criteria and the numerical example’s methods are more general than some existing results. A numerical example is given to illustrate the effectiveness of the proposed methods.