Chaotic dynamics in a simple predator-prey model with discrete delay

DOI10.3934/dcdsb.2020263zbMath1468.34111arXiv2007.16140OpenAlexW3082067544MaRDI QIDQ2026605

Gail S. K. Wolkowicz, Guihong Fan

Publication date: 20 May 2021

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.16140

zbMATH Keywords

uniform persistencepredator-prey modelbi-stabilityperiod doubling route to chaosHopf and saddle-node bifurcation of limit cyclesMackey-Glass attractorstage-structured model with maturation delay

Mathematics Subject Classification ID

Population dynamics (general) (92D25) Stability theory of functional-differential equations (34K20) Periodic solutions to functional-differential equations (34K13) Qualitative investigation and simulation of models involving functional-differential equations (34K60) Bifurcation theory of functional-differential equations (34K18) Complex (chaotic) behavior of solutions to functional-differential equations (34K23) Stationary solutions of functional-differential equations (34K21)

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Uses Software

• Maple
• Matlab
• XPPAUT

Cites Work

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• A detailed study of the Beddington-DeAngelis predator-prey model
• A predator-prey model in the chemostat with time delay
• Delay differential equations: with applications in population dynamics
• Existence and stability of solutions of a delay-differential system
• Introduction to functional differential equations
• A stage structured predator-prey model and its dependence on maturation delay and death rate
• Bifurcation and chaos of a delayed predator-prey model with dormancy of predators
• An alternative formulation for a delayed logistic equation
• Global Hopf branches and multiple limit cycles in a delayed Lotka-Volterra predator-prey model
• Geometric Stability Switch Criteria in Delay Differential Systems with Delay Dependent Parameters
• Simulating, Analyzing, and Animating Dynamical Systems
• Differential equation models of some parasitic infections: Methods for the study of asymptotic behavior
• Oscillation and Chaos in Physiological Control Systems
• Predator-prey Interactions with Delays Due to Juvenile Maturation
• CHAOS IN A THREE-DIMENSIONAL VOLTERRA–GAUSE MODEL OF PREDATOR–PREY TYPE
• An Introduction to Delay Differential Equations with Applications to the Life Sciences