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