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Bifurcations and chaotic analysis in a discrete predator-prey model with Ricker map
Jie Tian1, Lingling Liu2, Jiangqiong Yu1
1School of Mathematical Science, Chongqing Normal University, Chongqing 401331, People's Republic of China.
Chaos (Woodbury, N.Y.)
|July 10, 2026
Summary
This study explores a discrete predator-prey Ricker map model, investigating codimension-two bifurcations and chaos. Findings reveal complex population dynamics, including periodic and chaotic fluctuations, influenced by resonance phenomena.
Area of Science:
- Ecology
- Mathematical Biology
- Dynamical Systems
Background:
- Predator-prey models are crucial for understanding population dynamics.
- Previous research analyzed fixed-point stability and codimension-one bifurcations in Ricker map models.
- Codimension-two bifurcations and chaos in these models remain less explored.
Purpose of the Study:
- Investigate codimension-two bifurcations in a discrete predator-prey Ricker map model.
- Analyze 1:2, 1:3, and 1:4 resonances within the model.
- Examine the conditions for chaotic behavior using Marotto's definition.
Main Methods:
- Theoretical analysis of bifurcations.
- Numerical simulations to verify analytical findings.
- Application of Marotto's criterion for chaos detection.
Main Results:
- Identified codimension-two bifurcations associated with specific resonances.
- Demonstrated the existence of periodic and quasi-periodic behaviors.
- Confirmed the potential for chaotic dynamics under parameter variations.
Conclusions:
- Resonances in this predator-prey model lead to diverse population dynamics.
- The system can exhibit periodic fluctuations, long-period cycles, population outbreaks, and chaos.
- This research provides deeper insights into the complex interactions within discrete predator-prey systems.
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