A Three-Species Model With Predator-Taxis Sensitivity: Hopf Bifurcation and Active Control Stabilization
- Title
- A Three-Species Model With Predator-Taxis Sensitivity: Hopf Bifurcation and Active Control Stabilization
- Creator
- Chakraborty, Arkaprovo; Veeresha, P.; Trounev, Alexander; Jana, Debaldev
- Description
- This study presents an analysis of a novel fractional two preyone predator model incorporating predator-taxis sensitivity. We conduct a comprehensive stability analysis, explore the model's chaotic nature through period-doubling bifurcations, and also show the existence of limit cycles through fractional Hopf bifurcation. It is observed that the fractional-order parameter brings in a stabilizing effect and, simultaneously, a shift of the Hopf bifurcation point. At the Hopf bifurcation point, the system moves from stable equilibria to sustained oscillations. In addition, regardless of initial conditions, the system approaches a stable limit cycle, showing the robustness of the method. We also demonstrate the effectiveness of the active control method to eliminate the periodicity of the fractional system and also unravel the decelerating influence of the fractional-order parameter on the convergence time to equilibrium. These results provide valuable insights into the stabilization of ecosystem dynamics and contribute more broadly to our understanding of population dynamics in ecological systems. 2025 John Wiley & Sons Ltd.
- Source
- Mathematical Methods in the Applied Sciences;Volume;49;Issue;4;pp.2358-2370
- Date
- 01-01-2026
- Publisher
- John Wiley and Sons Ltd
- Subject
- active control method; fear effect; fractional Hopf bifurcation; predator-taxis sensitivity; stability analysis
- Coverage
- Chakraborty A., Center for Mathematical Needs, Department of Mathematics, CHRIST University, Bengaluru, India; Veeresha P., Center for Mathematical Needs, Department of Mathematics, CHRIST University, Bengaluru, India; Trounev A., Department of Mathematics, Kuban State Agrarian University, Krasnodar, Russian Federation; Jana D., Department of Mathematics, Ramakrishna Mission Vivekananda Educational and Research Institute, West Bengal, Howrah, India
- Rights
- Restricted Access; Hardcopy may be available in the library
- Relation
- ISSN: 1704214; CODEN: MMSCD
- Format
- online
- Language
- English
- Type
- Article
Collection
Citation
Chakraborty, Arkaprovo; Veeresha, P.; Trounev, Alexander; Jana, Debaldev, “A Three-Species Model With Predator-Taxis Sensitivity: Hopf Bifurcation and Active Control Stabilization,” CHRIST (Deemed To Be University) Institutional Repository, accessed June 18, 2026, https://archives.christuniversity.in/items/show/21789.