Bifurcations and dynamical behaviors for a generalized Maginu model with distributed delay

Xiaowei Ju ()
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Xiaowei Ju: Heilongjiang University of Science and Technology

Partial Differential Equations and Applications, 2025, vol. 6, issue 3, 1-24

Abstract: Abstract This paper is committed to study the dynamical behaviors of a generalized reaction-diffusion Maginu model with distributed delay. We investigate the stability of the positive equilibrium and the existence of periodic solutions bifurcating from the positive equilibrium. Further, by using the center manifold theorem and the normal form theory, we derive the precise conditions to judge the bifurcation direction and the stability of the bifurcating periodic solutions. Importantly, we deduce the exact conditions in terms of the diffusion coefficients to guarantee the occurrence of Turing instability for both homogeneous equilibrium solution and the Hopf bifurcating periodic solutions. Intuitively, numerical simulations are used to support our theoretical analysis.

Keywords: Generalized Maginu model; Distributed delay; Hopf bifurcating periodic solution; Turing instability; Equilibrium solution (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s42985-025-00330-5

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