Self-feedback delay induces extreme events in the theoretical Brusselator system

Area of Science:

• Theoretical chemistry
• Chemical kinetics
• Nonlinear dynamics

Background:

• The Brusselator model is a classic example of a reaction-diffusion system exhibiting complex dynamics.
• Time delays in chemical reactions can significantly alter system behavior, potentially leading to instability and extreme events.
• Understanding the impact of delays is crucial for predicting and controlling chemical processes.

Purpose of the Study:

• To investigate the influence of time-delayed self-feedback on the Brusselator model.
• To identify the conditions and mechanisms under which extreme events emerge in this system.
• To experimentally validate the theoretical predictions using an analog electronic circuit.

Main Methods:

• Theoretical analysis of the Brusselator model with time-delayed self-feedback.
• Stability analysis with respect to delay time.
• Numerical simulations using phase portraits, time series, and probability distribution functions.
• Two-parameter scans to map parameter regimes for extreme events and transient chaos.
• Construction and testing of an analog electronic circuit to emulate the model.

Main Results:

• Time delays in the Brusselator model can induce extreme events, both with and without diffusion.
• Stability analysis revealed the critical role of delay time in driving these extreme events.
• Numerical tools confirmed the occurrence of extreme events and identified regions of transient chaos.
• The analog electronic circuit successfully emulated the model's predicted dynamics, validating the theoretical findings.

Conclusions:

• Time-delayed self-feedback is a significant factor in the emergence of extreme events in the Brusselator model.
• The study provides a comprehensive understanding of the parameter space governing these phenomena.
• Experimental validation confirms the robustness of the theoretical model and its predictions.