Entropy driven mechanism for noise induced patterns formation in reaction-diffusion systems

TL;DR

This paper investigates how entropy-driven mechanisms and multiplicative noise induce and sustain stationary patterns in reaction-diffusion systems, revealing different pattern types at varying noise intensities through analysis and simulations.

Contribution

It introduces an entropy-driven framework for pattern formation in stochastic reaction-diffusion systems influenced by multiplicative noise, supported by analytical and simulation results.

Findings

Noise induces stationary patterns at intermediate intensities.

Unstable homogeneous states occur at low and high noise levels.

Three pattern types are identified: nucleation, spinodal decomposition, and stripe defects.

Abstract

We have studied the entropy-driven mechanism leading to stationary patterns formation in stochastic systems with local dynamics and non-Fickian diffusion. We have shown that a multiplicative noise fulfilling a fluctuation-dissipation relation is able to induce and sustain stationary structures with its intensity growth. It was found that at small and large noise intensities the system is characterized by unstable homogeneous states. At intermediate values of the noise intensity three types of patterns are possible: nucleation, spinodal decomposition and stripes with liner defects (dislocations). Our analytical investigations are verified by computer simulations.