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Second Order systems II

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In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.

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Programmable Spiral Wave Dynamics: Instability Cascades Driven by Temporal Modulation in a Reaction-Diffusion System.

Tarpan Maiti¹, Achal Jadhav¹, Pushpita Ghosh^1,2

¹School of Chemistry, Indian Institute of Science Education and Research, Thiruvananthapuram, Kerala 695551, India.

Journal of Chemical Theory and Computation

|September 19, 2025

Summary

This summary is machine-generated.

Periodic forcing of kinetic parameters in chemical models can control complex spiral wave behaviors. This study reveals how temporal instability drives diverse pattern formation, including spiral breakup and regeneration, in spatially stable systems.

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Area of Science:

Nonlinear dynamics
Chemical kinetics
Pattern formation

Background:

Spiral waves are key self-organizing structures in chemical and biological systems.
Instabilities of spirals in spatially inhomogeneous media are well-studied.
Response of spirals to temporal modulations near the Turing threshold is underexplored.

Purpose of the Study:

Investigate spiral wave instabilities induced by periodic forcing of kinetic parameters.
Explore pattern selection in a spatially stable yet temporally unstable regime.
Understand the transition from stable spirals to complex spatiotemporal dynamics.

Main Methods:

Utilized the Chlorine Dioxide-Iodine-Malonic Acid (CDIMA) model.
Applied periodic forcing to a kinetic parameter.
Analyzed spiral wave dynamics and pattern evolution.
Mapped observed phenomena onto a two-dimensional phase diagram.

Main Results:

Observed a cascade of modulation-induced phenomena: breathing spirals, core drift, breakup, and turbulence.
Identified transitions to oscillating clusters, Ising-front-like patterns, and bulk oscillations.
Discovered spiral regeneration with altered arm width and chirality reversal.
Revealed resonance-driven bifurcation cascades and amplitude-phase interactions leading to complex states.

Conclusions:

Periodic temporal forcing can unlock diverse and tunable spiral wave instabilities.
Simple temporal inputs can steer complex pattern selection in nonlinear chemical media.
Findings offer insights for systems chemistry, chemical wave control, and responsive self-organizing systems.