Reaction-Cattaneo systems with fluctuating relaxation time

Role of Noise-Modulated Self-Propulsion in Driving Spatiotemporal Orders in Active Systems

Fluctuations play a pivotal role in driving spatiotemporal order in active matter systems. In this study, we employ a novel analytical framework to investigate the impact of dichotomous noise on the self-propelling velocity of active particle systems such as polymerizing actin filaments or reproducing elongated bacteria. By incorporating dichotomous fluctuations with Ornstein-Zernike correlations into a continuum-based model, we derive a bifurcation condition in the noise parameter space, revealing a noise-induced instability that drives the emergence of traveling waves. This approach demonstrates how specific noise strengths and correlation times expand the instability region by introducing effective new degrees of freedom that alter the system's stability matrix. Advance numerical simulations, meticulously designed to handle the properties of dichotomous noise, validate these theoretical predictions and reveal excellent agreement. A key finding is the observation of wave-reversal behavior, driven by the sign alternation of the noise-modulated advection term and modulated by the relaxation time. Remarkably, we identify a finite parameter range where this reversal is suppressed, offering new insights into noise-induced bifurcations and spatiotemporal dynamics. Our combined analytical and numerical approach provides a deeper understanding of the role of noise in shaping self-organization and pattern formation in biological and synthetic active systems.

Unravelling diverse spatiotemporal orders in chlorine dioxide-iodine-malonic acid reaction-diffusion system through circularly polarized electric field and photo-illumination

Designing and predicting self-organized pattern formation in out-of-equilibrium chemical and biochemical reactions holds fundamental significance. External perturbations like light and electric fields exert a crucial influence on reaction-diffusion systems involving ionic species. While the separate impacts of light and electric fields have been extensively studied, comprehending their combined effects on spatiotemporal dynamics is paramount for designing versatile spatial orders. Here, we theoretically investigate the spatiotemporal dynamics of chlorine dioxide-iodine-malonic acid reaction-diffusion system under photo-illumination and circularly polarized electric field (CPEF). By applying CPEF at varying intensities and frequencies, we observe the predominant emergence of oscillating hexagonal spot-like patterns from homogeneous stable steady states. Furthermore, our study unveils a spectrum of intriguing spatiotemporal instabilities, encompassing stripe-like patterns, oscillating dumbbell-shaped patterns, spot-like instabilities with square-based symmetry, and irregular chaotic patterns. However, when we introduce periodic photo-illumination to the hexagonal spot-like instabilities induced by CPEF in homogeneous steady states, we observe periodic size fluctuations. Additionally, the stripe-like instabilities undergo alternating transitions between hexagonal spots and stripes. Notably, within the Turing region, the interplay between these two external influences leads to the emergence of distinct superlattice patterns characterized by hexagonal-and square-based symmetry. These patterns include parallel lines of spots, target-like formations, black-eye patterns, and other captivating structures. Remarkably, the simple perturbation of the system through the application of these two external fields offers a versatile tool for generating a wide range of pattern-forming instabilities, thereby opening up exciting possibilities for future experimental validation.

Thermodiffusion-induced traveling and shock waves in a colloidal solution

The formation of chemical waves in a nonlinear spatially extended system is one of the most fascinating far-from-equilibrium phenomena. An externally imposed thermal gradient in a liquid mixture may induce a concentration gradient generating a thermodynamic cross-flow, which is known as thermal diffusion or the Ludwig-Soret effect. The motion of the components of the mixture is governed by a nonlinear, partial differential equation for the density fraction in space and time. Here, we show that under an externally imposed constant thermal gradient, a traveling wave can emerge in a solution of self-propelled neutral colloid. An exact analytic solution of the spatially extended system is presented in one dimension for a constant thermal gradient to show the time development of a traveling wave. We analyze the effect of a small finite relaxation time of flux, which takes care of the finite inertia of the dispersing colloidal species. While the wave speed remains unaffected, the wave shape is significantly modified by the presence of the finite relaxation time of flux. Our result demonstrates that the traveling wave may reduce to a shock wave provided the product of the square of the wave speed and the relaxation time exactly balances the mass diffusion coefficient. This condition can be achieved by suitably adjusting the velocity of the emergent traveling wave by tuning the value of the constant thermal gradient and maintaining the appropriate boundary condition.

Delay-induced wave instabilities in single-species reaction-diffusion systems

The Turing (wave) instability is only possible in reaction-diffusion systems with more than one (two) components. Motivated by the fact that a time delay increases the dimension of a system, we investigate the presence of diffusion-driven instabilities in single-species reaction-diffusion systems with delay. The stability of arbitrary one-component systems with a single discrete delay, with distributed delay, or with a variable delay is systematically analyzed. We show that a wave instability can appear from an equilibrium of single-species reaction-diffusion systems with fluctuating or distributed delay, which is not possible in similar systems with constant discrete delay or without delay. More precisely, we show by basic analytic arguments and by numerical simulations that fast asymmetric delay fluctuations or asymmetrically distributed delays can lead to wave instabilities in these systems. Examples, for the resulting traveling waves are shown for a Fisher-KPP equation with distributed delay in the reaction term. In addition, we have studied diffusion-induced instabilities from homogeneous periodic orbits in the same systems with variable delay, where the homogeneous periodic orbits are attracting resonant periodic solutions of the system without diffusion, i.e., periodic orbits of the Hutchinson equation with time-varying delay. If diffusion is introduced, standing waves can emerge whose temporal period is equal to the period of the variable delay.

Nanosize pattern formation in overdamped stochastic reaction-diffusion systems with interacting adsorbate

We study overdamped stochastic model describing adsorption or desorption processes with nonequilibrium chemical reactions on the surface. It is shown that internal noise satisfying the fluctuation-dissipation relation at small intensities governs transitions between ordered thermodynamical dense and diluted phases. These phase transitions are characterized by an increase of fluctuations of the coverage filed and correlation radius of spatial modulation. At large noise intensity a transition towards disordered phase with chaotic spatial configuration is realized. We have shown that organized stationary patterns are of nanometer range. We define that both period of stationary structures and corresponding correlation radius depend on the noise intensity.

Controlling birhythmicity in a self-sustained oscillator by time-delayed feedback

Time-delayed feedback is a practical method for controlling various nonlinear dynamical systems. We consider its influence on the dynamics of a multicycle van der Pol oscillator that is birhythmic in nature. It has been shown that depending on the strength of delay the bifurcation space can be divided into two subspaces for which the dynamical response of the system is generically distinct. We observe an interesting collapse and revival of birhythmicity with the variation of the delay time. Depending on the parameter space the system also exhibits a transition between birhythmicity and monorhythmic behavior. Our analysis of amplitude equation corroborates with the results obtained by numerical simulation of the dynamics.