Relaxation oscillations for Leslie-type predator-prey model with Holling type I response functional function

DOI10.1016/j.aml.2021.107328zbMath1480.34064OpenAlexW3154013978WikidataQ115597744 ScholiaQ115597744MaRDI QIDQ2233337

Shimin Li, Kuilin Wu, Xiao-Ling Wang, Xiao-Li Li

Publication date: 15 October 2021

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2021.107328

zbMATH Keywords

slow-fast systempredator-prey systemgeometric singular perturbation theoryrelaxation oscillation

Mathematics Subject Classification ID

Population dynamics (general) (92D25) Discontinuous ordinary differential equations (34A36) Qualitative investigation and simulation of ordinary differential equation models (34C60) Singular perturbations for ordinary differential equations (34E15) Relaxation oscillations for ordinary differential equations (34C26)

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Global Stability and Canard Explosions of the Predator-Prey Model with the Sigmoid Functional Response, Oscillatory and transient dynamics of a slow-fast predator-prey system with fear and its carry-over effect, On the monotonicity of limit wave speed of the pgKdV equation with nonlinear terms of arbitrary higher degree, Multiple bifurcations in a discrete Bazykin predator-prey model with predator intraspecific interactions and ratio-dependent functional response, Super-explosion and inverse canard explosion in a piecewise-smooth slow-fast Leslie-Gower model, Bifurcation of a discrete predator-prey model with increasing functional response and constant-yield prey harvesting

Cites Work

• Unnamed Item
• A predator-prey model with a Holling type I functional response including a predator mutual interference
• Relaxation oscillations and canard explosion in a predator-prey system of Holling and Leslie types
• Bifurcation analysis of modified Leslie-Gower predator-prey model with Michaelis-Menten type prey harvesting
• Canard cycles for predator-prey systems with Holling types of functional response
• On bifurcation delay: an alternative approach using geometric singular perturbation theory
• Phase portraits, Hopf bifurcations and limit cycles of Leslie-Gower predator-prey systems with harvesting rates
• Limit cycles in slow-fast forest-pest models
• Canard phenomenon in a slow-fast modified Leslie-Gower model
• Relaxation oscillations in a slow-fast modified Leslie-Gower model
• Relaxation oscillations in a class of predator-prey systems.
• Singular perturbations of the Holling I predator-prey system with a focus
• Relaxation oscillations of a slow-fast predator-prey model with a piecewise smooth functional response
• Bifurcations in a predator-prey system of Leslie type with generalized Holling type III functional response
• Nonlinear oscillations in the modified Leslie-Gower model
• The entry-exit theorem and relaxation oscillations in slow-fast planar systems
• Uniqueness of limit cycles for sewing planar piecewise linear systems
• Necessary and sufficient conditions for the nonexistence of limit cycles of Leslie-Gower predator-prey models
• A comparison of two predator-prey models with Holling's type I functional response
• The Bifurcation Structure of the Holling--Tanner Model for Predator-Prey Interactions Using Two-Timing
• Number and Stability of Relaxation Oscillations for Predator-Prey Systems with Small Death Rates
• Hopf Cyclicity and Global Dynamics for a Predator–Prey System of Leslie Type with Simplified Holling Type IV Functional Response
• DYNAMIC ANALYSIS OF A HOLLING I PREDATOR-PREY SYSTEM WITH MUTUAL INTERFERENCE CONCERNING PEST CONTROL
• SOME FURTHER NOTES ON THE USE OF MATRICES IN POPULATION MATHEMATICS
• The entry-exit function and geometric singular perturbation theory