Hopf bifurcation of a delayed reaction-diffusion model with advection term

Article Mathematics, Applied

Hopf bifurcation of a diffusive SIS epidemic system with delay in heterogeneous environment

Dan Wei et al.

Summary: This paper provides an in-depth qualitative analysis of the dynamic behavior of a diffusive SIS epidemic system with delay in a heterogeneous environment under homogeneous Neumann boundary condition. It explores the stability and effects of nonhomogeneous coefficients on disease-free equilibrium, as well as the existence, multiplicity, and structure of endemic equilibrium. The paper also analyzes the stability of endemic equilibrium, the existence of Hopf bifurcations, and the direction and stability of bifurcating periodic solutions.

APPLICABLE ANALYSIS (2022)

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Article Mathematics, Applied

Stability and bifurcation in a two-species reaction-diffusion-advection competition model with time delay

Li Ma et al.

Summary: This paper investigates the dynamics of a class of two-species reaction-diffusion-advection competition models with time delay in a bounded domain, subject to homogeneous Dirichlet or no-flux boundary conditions. The study explores the existence of steady state solutions using the Lyapunov-Schmidt reduction method, and analyzes the stability and Hopf bifurcation at spatially nonhomogeneous steady states. Furthermore, the effect of advection on Hopf bifurcation is examined, revealing that an increase in convection rate makes the Hopf bifurcation phenomenon more likely to occur.

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS (2021)

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Article Mathematics, Applied

POSITIVE SOLUTIONS IN THE COMPETITIVE LOTKA-VOLTERRA REACTION-DIFFUSION MODEL WITH ADVECTION TERMS

Li Ma et al.

Summary: This paper focuses on the existence, uniqueness, and global asymptotical stability of the coexistence steady state for a competitive Lotka-Volterra reaction-diffusion model with advection term in ecology. The approaches utilized include monotone dynamical systems theory, sub-super solutions method, principal spectral theory, and other nontrivial analytic skills.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY (2021)

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Article Mathematics