The continuous predator-prey model is one of the main models studied in recent years. The dynamical properties of these models are so complex that it is an urgent topic to be studied. In this paper, we transformed a continuous predator-prey model with modified Leslie-Gower and Hollingtype III schemes into a discrete mode by using Euler approximation method. The existence and stability of fixed points for this discrete model were investigated. Flip bifurcation analyses of this discrete model was carried out and corresponding bifurcation conditions were obtained. Provided with these bifurcation conditions, an example was given to carry out numerical simulations, which shows that the discrete model undergoes flip bifurcation around the stable fixed point. In addition, compared with previous studies on the continuous predator-prey model, our discrete model shows more irregular and complex dynamic characteristics. The present research can be regarded as the continuation and development of the former studies.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.3934/mbe.2020106 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Importance of pesticide and additional food in pest-predator system: a theoretical study.
J Biol Dyn
December 2025
Department of Life Sciences, Sri Sathya Sai University for Human Excellence, Kalaburagi, India.
Integrated pest management (IPM) combines chemical and biological control to maintain pest populations below economic thresholds. The impact of providing additional food for predators on pest-predator dynamics, along- side pesticide use, in the IPM context remains unstudied. To address this issue, in this work a theoretical model was developed using differential equations, assuming Holling type II functional response for the predator, with additional food sources included.
View Article and Find Full Text PDFDynamic patterns in herding predator-prey system: Analyzing the impact of inertial delays and harvesting.
Chaos
December 2024
Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India.
This study expands traditional reaction-diffusion models by incorporating hyperbolic dynamics to explore the effects of inertial delays on pattern formation. The kinetic system considers a harvested predator-prey model where predator and prey populations gather in herds. Diffusion and inertial effects are subsequently introduced.
View Article and Find Full Text PDFAbstractInducible defenses can affect the persistence, structure, and stability of consumer-resource systems. Theory shows that these effects depend on characteristics of the inducible defense, including timing, costs, efficacy, and sensitivity to consumer density. However, the expression and costs of inducible defenses often vary among life stages, which has not been captured in previous unstructured models.
View Article and Find Full Text PDFCombined impact of fear and Allee effect in predator-prey interaction models on their growth.
Math Biosci Eng
October 2024
Department of Mathematics and Statistics, University of Strathclyde, UK.
We considered predator-prey models which incorporated both an Allee effect and a new fear factor effect together, and where the predator predated the prey with a Holling type I functional response. We started off with a two-dimensional model where we found possible equilibria and examined their stabilities. By using the predator mortality rate as the bifurcation parameter, the model exhibited Hopf-bifurcation for the coexistence equilibrium.
View Article and Find Full Text PDFMost Random-Encounter-Model Density Estimates in Camera-Based Predator-Prey Studies Are Unreliable.
Animals (Basel)
November 2024
U.S. Geological Survey, Western Ecological Research Center, Boulder City, NV 89005, USA.
Identifying population-level relationships between predators and their prey is often predicated on having reliable population estimates. Camera-trapping is effective for surveying terrestrial wildlife, but many species lack individually unique natural markings that are required for most abundance and density estimation methods. Analytical approaches have been developed for producing population estimates from camera-trap surveys of unmarked wildlife; however, most unmarked approaches have strict assumptions that can be cryptically violated by survey design characteristics, practitioner choice of input values, or species behavior and ecology.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!