Investigating the Dynamic Behavior of Integer and Noninteger Order System of Predation with Holling’s Response
Abstract
:1. Introduction
2. Main Model and Its Mathematical Analysis
2.1. Boundness
2.2. Existence and Stability of Equilibria
- (a)
- in the case of the system of predation (4) has two nontrivial points;
- (b)
- in the case the dynamic model has a unique interior state;
- (c)
- for condition the predator–prey model has no interior steady state;
2.3. Local Bifurcation Analysis
2.3.1. Transcritical Bifurcation
2.3.2. Saddle-Node Bifurcation
2.3.3. Hopf Bifurcation
3. Fractional Predator–Prey Model of Reaction–Diffusion Type and Its Method of Approximation
Numerical Approximation Method
- given , compute with the aid of definition (55);
- define to be ;
- compute (that is, the derivative of function ) on the grid by applying (56).
4. Numerical Experiment and Results
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Owolabi, K.M.; Jain, S.; Pindza, E. Investigating the Dynamic Behavior of Integer and Noninteger Order System of Predation with Holling’s Response. Mathematics 2024, 12, 1530. https://doi.org/10.3390/math12101530
Owolabi KM, Jain S, Pindza E. Investigating the Dynamic Behavior of Integer and Noninteger Order System of Predation with Holling’s Response. Mathematics. 2024; 12(10):1530. https://doi.org/10.3390/math12101530
Chicago/Turabian StyleOwolabi, Kolade M., Sonal Jain, and Edson Pindza. 2024. "Investigating the Dynamic Behavior of Integer and Noninteger Order System of Predation with Holling’s Response" Mathematics 12, no. 10: 1530. https://doi.org/10.3390/math12101530
APA StyleOwolabi, K. M., Jain, S., & Pindza, E. (2024). Investigating the Dynamic Behavior of Integer and Noninteger Order System of Predation with Holling’s Response. Mathematics, 12(10), 1530. https://doi.org/10.3390/math12101530