Normal form formulations of double-Hopf bifurcation for partial functional differential equations with nonlocal effect

DOI10.1016/j.jde.2021.11.046zbMath1480.35020OpenAlexW4200114666MaRDI QIDQ2062052

Yanyan Li

Publication date: 22 December 2021

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2021.11.046

zbMATH Keywords

quasi-periodic solutionpartial functional differential equationsnonlocal effectdouble-Hopf bifurcationHolling-Tanner predator-prey modelmulti-periodic solution

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Partial functional-differential equations (35R10) Almost and pseudo-almost periodic solutions to PDEs (35B15) Bifurcations in context of PDEs (35B32) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10) Semilinear parabolic equations (35K58)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dynamics and pattern formation in a diffusive predator-prey system with strong Allee effect in prey
• Hopf bifurcation in a delayed reaction-diffusion-advection population model
• Local vs. non-local interactions in population dynamics
• Double zero singularity and spatiotemporal patterns in a diffusive predator-prey model with nonlocal prey competition
• Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system
• Hopf bifurcations in a reaction-diffusion population model with delay effect
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Introduction to functional differential equations
• Study of double Hopf bifurcation and chaos for an oscillator with time delayed feedback
• Patterns in a nonlocal time-delayed reaction-diffusion equation
• Theory and applications of partial functional differential equations
• Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation
• A predator-prey reaction-diffusion system with nonlocal effects
• Spatiotemporal patterns in a reaction-diffusion model with the Degn-Harrison reaction scheme
• Instabilities and spatiotemporal patterns behind predator invasions with nonlocal prey competition
• Double Hopf bifurcation in delayed reaction-diffusion systems
• Formulation of the normal form of Turing-Hopf bifurcation in partial functional differential equations
• Spatiotemporal dynamics in the single population model with memory-based diffusion and nonlocal effect
• Stability and spatiotemporal dynamics in a diffusive predator-prey model with nonlocal prey competition
• Stability and bifurcation in a reaction-diffusion model with nonlocal delay effect
• Stability and bifurcation on predator-prey systems with nonlocal prey competition
• Population dynamic models with nonlocal delay on bounded domains and their numerical computations
• Spatio-temporal pattern formation in a nonlocal reaction-diffusion equation
• Secondary Bifurcation in Neuronal Nets
• Centre manifolds for partial differential equations with delays
• Double Hopf Bifurcations in the Differentially Heated Rotating Annulus
• Bifurcations and spatiotemporal patterns in a ratio‐dependent diffusive Holling‐Tanner system with time delay
• On the analysis of the double Hopf bifurcation in machining processes via centre manifold reduction
• Smoothness of Center Manifolds for Maps and Formal Adjoints for Semilinear FDEs in General Banach Spaces
• Normal forms and Hopf bifurcation for partial differential equations with delays
• Analysis of a Local Diffusive SIR Model with Seasonality and Nonlocal Incidence of Infection
• Diffusive spatial movement with memory and maturation delays
• Transient oscillatory patterns in the diffusive non-local blowfly equation with delay under the zero-flux boundary condition

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