Related Experiment Video
Updated: Jan 7, 2026

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
Published on: July 4, 2007
Application of a class of difference equations in population dynamics
Changtong Li1, Jia Tian1, Mengxuan Ma2
1School of Science, Xi'an Technological University, No. 2 Xuefuzhonglu Road, Weiyang District, Xi'an, Shaanxi 710021, People's Republic of China.
Abstract:
Difference equations have far-reaching implications across various disciplines, particularly in biology. Recent studies have revealed that discrete biological mathematical systems exhibit intricate and complex dynamic behaviors. This paper investigates the stability and bifurcation dynamics of a discrete predator-prey model with a Holling-II type functional response and a nonlinear Michaelis-Menten type harvesting. We employed the semi-discretization method to derive the discrete system and analyzed the existence and local stability of the fixed points. By employing the center manifold theorem and bifurcation theory, we deduced the transcritical bifurcation conditions at the boundary fixed points E1, E2, and E3, as well as the Neimark-Sacker bifurcation conditions at the positive fixed point E4. Numerical simulation validated the correctness of our theoretical analysis and further elucidated the system's dynamic behaviors, including the transitions in the stability of fixed points and the Neimark-Sacker bifurcation phenomena.
Related Concept Videos
Population Growth
Exponential Equations for Modeling Growth
Difference Equation Solution using z-Transform
The z-transform facilitates handling delayed signals by shifting the signal in the z-domain, which corresponds to delaying the signal in the time domain, and advancing signals by similarly shifting in the...
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 from...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Exponential Equations with Logarithms: Problem Solving

