On the Role of Diffusion Behaviors in Stability Criterion forp-Laplace Dynamical Equations with Infinite Delay and Partial Fuzzy Parameters under Dirichlet Boundary Value

Abstract

By the way of Lyapunov-Krasovskii functional approach and some variational methods in the Sobolev spaceW01,p(Ω), a global asymptotical stability criterion forp-Laplace partial differential equations with partial fuzzy parameters is derived under Dirichlet boundary condition, which gives a positive answer to an open problem proposed in some related literatures. Different from many previous related literatures, the nonlinearp-Laplace diffusion item plays its role in the new criterion though the nonlinearp-Laplace presents great difficulties. Moreover, numerical examples illustrate that our new stability criterion can judge what the previous criteria cannot do.

New Stability Criterion for Takagi‐Sugeno Fuzzy Cohen‐Grossberg Neural Networks with Probabilistic Time‐Varying Delays

“…Since the stability of nonlinear -Laplacian diffusion neural networks was originally investigated in [2], various -Laplacian diffusion neural networks have attracted a lot of interest ( [6,17,34,39,44]). As pointed out in Discussion 1, some new conditions and methods may not be applicable to CGNNs model with nonlinear -Laplacian diffusion.…”

“…In Theorem 6, (22) illustrates the influence of nonlinear diffusion on the stability of system (8) while its role was always ignored in existing results (see, e.g., [5,39,44]). …”

Robust Stability of Nonlinear Diffusion Fuzzy Neural Networks with Parameter Uncertainties and Time Delays

“…The Lyapunov functionals (33) and (34) are similar to the quadric form different from those of [11,13,14,20]. Actually, the quadric form and matrix form help us to derive the LMI-based criterion.…”

“…The boundedness of amplification functions a i and a j may be unbounded while amplification functions are always proposed to be bounded in many existing results (see, e.g., [7,9,[18][19][20][21]). …”