Coupling-induced tunable oscillations in loops of even-numbered bistable systems

Area of Science:

• Nonlinear Dynamics
• Complex Systems
• Oscillatory Systems

Background:

• Bistable oscillators with negative couplings can exhibit asymmetric repulsions, leading to sustained oscillations.
• Previous research focused on odd-numbered oscillators and asymmetric behaviors.

Purpose of the Study:

• To investigate the induction of traveling-like oscillations in even-numbered overdamped bistable oscillators.
• To explore the effect of changing negative couplings to positive ones.
• To elucidate the conditions and parameters governing these symmetric oscillations.

Main Methods:

• Utilized a simple two-state model for analysis.
• Performed numerical simulations to validate findings.
• Analyzed relationships between oscillation amplitude, frequency, and coupling strength.

Main Results:

• Positive couplings in even-numbered bistable oscillators create symmetric attractions.
• Identified specific symmetric initial conditions required for sustained oscillations.
• Estimated the necessary coupling strength ranges for oscillation maintenance.
• Observed consistency between theoretical analysis and numerical results regarding amplitude and frequency.

Conclusions:

• Coupling-induced oscillations can be achieved in even-numbered bistable systems through symmetric attractions.
• Findings expand the understanding of oscillatory behaviors in coupled nonlinear systems.
• The study provides insights into controlling and predicting traveling-like wave phenomena in such systems.