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Exploring the dynamics of conjugate coupled Chua circuits: simulations and experiments
Tanu Singla1, Nitin Pawar, P Parmananda
1Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India.
Summary
Coupling two Chua circuits can either suppress oscillations, causing amplitude death, or induce oscillations, known as rhythmogenesis, depending on their initial states. The coupling strength effectively controls these dynamics in both identical and nonidentical systems.
Area of Science:
- Nonlinear dynamics
- Complex systems
- Circuit theory
Background:
- Chua circuits are fundamental nonlinear systems used to study complex dynamical behaviors.
- Coupling autonomous systems can lead to emergent phenomena not present in individual components.
- Amplitude death and rhythmogenesis are key concepts in understanding coupled oscillator dynamics.
Purpose of the Study:
- To investigate the effects of conjugate variable coupling on the dynamics of two Chua circuits.
- To explore the emergence of amplitude death and rhythmogenesis in mutually coupled Chua circuits.
- To determine the influence of system parameters and coupling strength on observed phenomena.
Main Methods:
- Numerical simulations of coupled Chua circuit equations.
- Experimental verification using physical Chua circuit implementations.
- Analysis of system trajectories in phase space.
- Systematic variation of coupling parameters and initial conditions.
Main Results:
- Conjugate coupling induced amplitude death when circuits were initially in the oscillatory regime.
- Conjugate coupling induced rhythmogenesis when circuits were initially in quiescent (fixed-point) states.
- Both phenomena were observed for identical and nonidentical Chua circuits.
- The magnitude of conjugate coupling was found to efficiently regulate the system dynamics.
Conclusions:
- Mutually coupled Chua circuits exhibit rich dynamical behaviors including amplitude death and rhythmogenesis.
- The initial state of the autonomous systems dictates the outcome of conjugate coupling.
- Conjugate coupling offers a viable mechanism for controlling complex dynamics in coupled nonlinear systems.
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