Related Experiment Video
Updated: Apr 30, 2026

A Real-Time Interactive System for Studying Confrontational Pursuit Behavior in Rodents
Published on: May 16, 2025
Global hopf bifurcation on two-delays leslie-gower predator-prey system with a prey refuge
Qingsong Liu1, Yiping Lin1, Jingnan Cao2
1Department of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650500, China.
Abstract:
A modified Leslie-Gower predator-prey system with two delays is investigated. By choosing τ 1 and τ 2 as bifurcation parameters, we show that the Hopf bifurcations occur when time delay crosses some critical values. Moreover, we derive the equation describing the flow on the center manifold; then we give the formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the theoretical results and chaotic behaviors are observed. Finally, using a global Hopf bifurcation theorem for functional differential equations, we show the global existence of the periodic solutions.
Related Concept Videos
Predator-Prey Interactions
Optimal Foraging
Root Loci for Positive-Feedback Systems
The construction rules for the root locus in positive feedback systems are similar to those in...
Second Order systems II
Speciation Rates
Transmission-Line Differential Equations
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured...

