Resonance tongues and patterns in periodically forced reaction-diffusion systems

Area of Science:

• Chemical kinetics
• Nonlinear dynamics
• Pattern formation

Background:

• The Belousov-Zhabotinsky (BZ) reaction is a classic example of a chemical oscillator exhibiting complex spatiotemporal patterns.
• Unforced BZ systems display uniform oscillations and rotating spiral waves.
• External periodic forcing can significantly alter the emergent dynamics of reaction-diffusion systems.

Purpose of the Study:

• To investigate the formation of resonant and near-resonant patterns in a light-sensitive BZ reaction under periodic optical forcing.
• To identify the parameter regimes (frequency and amplitude) that lead to specific resonant pattern formations.
• To compare the observed patterns with those predicted by a related theoretical model.

Main Methods:

• Experimental analysis of a light-sensitive BZ reaction subjected to spatially homogeneous, time-periodic light perturbations.
• Characterization of emergent patterns by analyzing their temporal response across different forcing frequencies and amplitudes.
• Numerical simulations using a forced FitzHugh-Nagumo reaction-diffusion model to corroborate experimental findings.

Main Results:

• Resonant and near-resonant pattern formation was observed in the forced BZ system.
• Specific parameter regions (tongues) for resonance were identified in the forcing frequency-amplitude plane.
• Forced system patterns included standing-wave labyrinths and rotating spiral waves, distinct from the unforced system's dynamics.
• The type of resonant response (near uniform oscillation frequency or spiral wave frequency) influenced the observed patterns.
• Numerical simulations of the FitzHugh-Nagumo model reproduced similar resonant and near-resonant patterns.

Conclusions:

• Periodic light forcing induces diverse resonant and near-resonant spatiotemporal patterns in the light-sensitive BZ reaction.
• The system's response depends critically on the forcing parameters (amplitude and frequency) and the intrinsic frequencies of the unforced system.
• The FitzHugh-Nagumo model serves as a valid theoretical framework for understanding the complex dynamics observed in the forced BZ system.
• This study elucidates the rich pattern-forming capabilities of oscillating chemical systems under external periodic stimuli.