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Stability of ecosystems under oscillatory driving with frequency modulation
Subhendu Bhandary1, Tanmoy Banerjee2, Partha Sharathi Dutta1
1Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140 001, Punjab, India.
Physical Review. E
|September 19, 2023
Summary
Frequency modulation of seasonal forcing can stabilize consumer-resource cycles, leading to stable synchronized solutions. Increased modulation strength enhances stability, with intermittent synchronization also observed in ecosystem dynamics.
Area of Science:
- Ecology
- Systems Biology
- Mathematical Modeling
Background:
- Consumer-resource cycles are fundamental to ecosystem dynamics.
- Seasonal forcing significantly impacts ecosystem stability, but typically studied at constant frequencies.
- The effect of time-varying frequencies on ecosystem stability remains underexplored.
Purpose of the Study:
- To investigate the impact of frequency modulation in seasonal forcing on consumer-resource ecosystem stability.
- To analyze how time-varying frequencies influence synchronized and asynchronous dynamics in ecological networks.
Main Methods:
- Utilized isolated and network models of cyclic consumer-resource ecosystems.
- Applied oscillatory driving with frequency modulation.
- Employed the maximal Lyapunov exponent to assess the stability of synchronous solutions.
- Used the phase-reduction method to derive a phase equation for network models.
Main Results:
- Frequency modulation can induce stable synchronized solutions in consumer-resource ecosystems.
- System stability increases with modulation strength, with a higher fraction of stable synchronous solutions observed.
- Uncovered intermittent synchronization, characterized by alternating synchronous and asynchronous dynamics.
- Network topology, specifically rewiring probability, showed a negligible effect on the stability of synchronous solutions.
Conclusions:
- Frequency modulation is a critical factor in regulating ecosystem stability under seasonal perturbations.
- The findings provide a deeper understanding of ecological network responses to dynamic environmental forcing.
- Stable synchronized states can be achieved through controlled frequency modulation of external drivers.
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