Global dynamics for a class of reaction-diffusion equations with\n distributed delay and Neumann condition

2018/10/01 by Tarik Mohammed Touaoula, Touaoula, Tarik Mohammed
Computer Science · Engineering · Medicine · #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1810.00975

openalex publication_date 2018/10/01 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate a class of non-monotone reaction-diffusion\nequations with distributed delay and a homogenous boundary Neumann condition,\nwhich have a positive steady state. The main concern is the global attractivity\nof the unique positive steady state. To achieve this, we use an argument of a\nsub and super-solution combined with fluctuation method. We also give a\ncondition for which the exponential stability of the positive steady state is\nreached. As an example, we apply our results to diffusive Nicholson blowflies\nand diffusive Mackey-Glass equation with distributed delay. We point out that\nwe obtain some new results on exponential stability of the positive steady\nstate for these cited models.\n

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