Pulse-coupled BZ oscillators with unequal coupling strengths.

Area of Science:

• Chemical kinetics
• Nonlinear dynamics
• Complex systems

Background:

• Coupled chemical oscillators typically use symmetric coupling.
• Asymmetric connectivity is crucial in biological systems like neural networks.
• Manipulating connection strengths in reciprocal coupling is challenging.

Purpose of the Study:

• Investigate asymmetric coupling in identical, pulse-coupled Belousov-Zhabotinsky (BZ) oscillators.
• Analyze the impact of unequal connection strengths on oscillatory behavior.
• Explore novel temporal patterns arising from asymmetric interactions.

Main Methods:

• Utilized two identical, pulse-coupled Belousov-Zhabotinsky (BZ) oscillators.
• Employed asymmetric pulse perturbations containing KBr (inhibitor) and AgNO3 (excitatory).
• Investigated the effects of time delay on system dynamics.

Main Results:

• Observed simple out-of-phase, complex oscillations, and oscillatory-suppressed states.
• Discovered temporally periodic N:M patterns due to long-term inhibitory effects.
• Identified a novel 1:N pattern (double peak start) with excitatory coupling, time delay, and high AgNO3 concentration.
• Found that time delay has minimal qualitative impact on asymmetric inhibitory coupling.

Conclusions:

• Asymmetric coupling in BZ oscillators leads to complex and novel temporal patterns.
• The long-term effects of inhibitory pulses are critical for N:M pattern formation.
• Excitatory asymmetric coupling with delay can generate unique dynamics.
• Numerical simulations validate theoretical predictions for asymmetric pulse-coupled systems.