Asymptotic behavior of a neural field lattice model with a Heaviside operator

作者：Han, Xiaoying^*; Kloeden, Peter E.

来源：Physica D: Nonlinear Phenomena , 2019, 389: 1-12.

DOI：10.1016/j.physd.2018.09.004

• Neuron networks
• Neural field lattice model
• Differential inclusion
• Nonautonomous set-valued dynamical system
• Pullback attractor
• Forward omega limit set

Motivated by the importance of discrete structures of neuron networks, a neural field lattice system arising from the discretization of neural field models in the form of integro-differential equations is studied. The neural field lattice system is first formulated as a differential inclusion on a weighted space of infinite sequences, due to the switching effects. Then the existence of solutions of the resulting differential inclusion is proved by a series of sequential finite-dimensional approximations. The solutions are shown to generate a nonautonomous set-valued dynamical system which possesses a pullback attractor. Forward omega limit sets for the set-valued dynamical system are also discussed.

• 出版日期2019-2
• 单位华中科技大学