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How to obtain extreme multistability in coupled dynamical systems
C R Hens1, R Banerjee, U Feudel
1Central Instrumentation, CSIR-Indian Institute of Chemical Biology, Kolkata, India
Summary
Researchers developed a method for coupling dynamical systems to achieve extreme multistability, enabling infinite coexisting attractors. This robust phenomenon is demonstrated in various models, highlighting its general applicability in coupled systems.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Complex Systems
Background:
- Multistability, the coexistence of multiple stable states, is a key feature in nonlinear dynamical systems.
- Extreme multistability, characterized by an infinite number of coexisting attractors, presents unique challenges and opportunities in understanding complex system behavior.
- Designing coupling schemes to reliably induce and control extreme multistability remains an open research area.
Purpose of the Study:
- To introduce a general method for designing coupling schemes to realize extreme multistability in dynamical systems.
- To demonstrate the flexibility and broad applicability of the proposed coupling method.
- To investigate the robustness of extreme multistability in the presence of parameter variations.
Main Methods:
- Utilizing the concept of partial synchronization, guided by Lyapunov function stability, to engineer coupling strategies.
- Applying the developed method to diverse dynamical models, including the Rössler system and a chemical oscillator.
- Analyzing the system's behavior under parameter mismatch to assess the robustness of the observed extreme multistability.
Main Results:
- Successfully designed coupling schemes that lead to the coexistence of infinitely many attractors for specific parameter sets.
- Demonstrated the generality of the method, showing its applicability across different types of dynamical systems.
- Confirmed that extreme multistability is a robust phenomenon, persisting even with parameter mismatches.
Conclusions:
- The proposed method provides a flexible and general approach for achieving extreme multistability in coupled dynamical systems.
- Partial synchronization based on Lyapunov stability is an effective strategy for inducing and controlling extreme multistability.
- Extreme multistability is a widespread and robust phenomenon in coupled nonlinear systems.
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