Understanding and shaping the dynamics of neural architectures with uncertainty, memory, and spatial interactions is a fundamental problem in neural networks and adaptive systems. In particular, controlled destabilization plays an important role in promoting exploration, adaptability, and non-stationary behavior, yet remains far less studied than stabilization and convergence. In this paper, we investigated destabilizing dynamics in a class of space–time discrete fuzzy multidirectional associative memory (MAM) neural networks with time-varying delays and diffusion effects. Such networks integrate fuzzy rule-based representations, delayed feedback, and spatial coupling, and are relevant to adaptive control, associative memory, and multi-agent dynamical systems. We first established the existence of equilibrium states by using topological degree theory, which provides a rigorous foundation for the subsequent analysis. Then, by designing localized Dirichlet boundary feedback mechanisms and constructing novel discrete Lyapunov–Krasovskii functionals with delay-dependent double-sum terms, we derived verifiable sufficient conditions for global asymptotic and exponential anti-stabilization. These results characterize how diffusion intensity, fuzzy parameters, and self-inhibition coefficients influence destabilizing behavior and determine the rate of divergence from equilibrium. The proposed framework provides new theoretical insights into anti-stabilization dynamics in discrete spatiotemporal fuzzy neural networks. Numerical examples further support the theoretical analysis and demonstrate the effectiveness of the proposed approach.
Citation: Bin Wang. Anti-stabilizing dynamics in fuzzy multidirectional associative memory neural networks with discrete spatiotemporal structure[J]. Networks and Heterogeneous Media, 2026, 21(3): 915-942. doi: 10.3934/nhm.2026038
Understanding and shaping the dynamics of neural architectures with uncertainty, memory, and spatial interactions is a fundamental problem in neural networks and adaptive systems. In particular, controlled destabilization plays an important role in promoting exploration, adaptability, and non-stationary behavior, yet remains far less studied than stabilization and convergence. In this paper, we investigated destabilizing dynamics in a class of space–time discrete fuzzy multidirectional associative memory (MAM) neural networks with time-varying delays and diffusion effects. Such networks integrate fuzzy rule-based representations, delayed feedback, and spatial coupling, and are relevant to adaptive control, associative memory, and multi-agent dynamical systems. We first established the existence of equilibrium states by using topological degree theory, which provides a rigorous foundation for the subsequent analysis. Then, by designing localized Dirichlet boundary feedback mechanisms and constructing novel discrete Lyapunov–Krasovskii functionals with delay-dependent double-sum terms, we derived verifiable sufficient conditions for global asymptotic and exponential anti-stabilization. These results characterize how diffusion intensity, fuzzy parameters, and self-inhibition coefficients influence destabilizing behavior and determine the rate of divergence from equilibrium. The proposed framework provides new theoretical insights into anti-stabilization dynamics in discrete spatiotemporal fuzzy neural networks. Numerical examples further support the theoretical analysis and demonstrate the effectiveness of the proposed approach.
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Bin Wang. Anti-stabilizing dynamics in fuzzy multidirectional associative memory neural networks with discrete spatiotemporal structure[J]. Networks and Heterogeneous Media, 2026, 21(3): 915-942. doi: 10.3934/nhm.2026038
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