Related papers: Revealing new dynamical patterns in a reaction-dif…
Pattern formation in reaction-diffusion systems is of great importance in surface micro-patterning [Grzybowski et al. Soft Matter. 1, 114 (2005)], self-organization of cellular micro-organisms [Schulz et al. Annu. Rev. Microbiol. 55, 105…
An inherent fragility of quadrotor systems stems from model inaccuracies and external disturbances. These factors hinder performance and compromise the stability of the system, making precise control challenging. Existing model-based…
Spatial self-organization emerges in distributed systems exhibiting local interactions when nonlinearities and the appropriate propagation of signals are at work. These kinds of phenomena can be modeled with different frameworks, typically…
Spatial pattern formation is a key feature of many natural systems in physics, chemistry and biology. The essential theoretical issue in understanding pattern formation is to explain how a spatially homogeneous initial state can undergo…
Chemical waves constitute a known class of dissipative structures emerging in reaction-diffusion systems. They play a crucial role in biology, spreading information rapidly to synchronize and coordinate biological events. We develop a…
We explore a mechanism of pattern formation arising in processes described by a system of a single reaction-diffusion equation coupled with ordinary differential equations. Such systems of equations arise from the modeling of interactions…
Lotka's seminal work (A.J. Lotka A., Proc. Natl. Acad. Sci. U.S.A. 6 (1920) 410) "on certain rhythmic relations'' is already one hundred years old, but the research activity about pattern formations due to cyclical dominance is more vibrant…
A molecule traveling in a realistic propagation environment can experience stochastic interactions with other molecules and the environment boundary. The statistical behavior of some isolated phenomena, such as dilute unbounded molecular…
We consider a couple of models for the dynamics of the populations of two interacting species, inspired by Lotka-Volterra's classical equations. The novelty of this work is that the interaction terms are non local and the interaction occurs…
This paper investigates the conditions for the stability and emergence of patterns in a new three-component reaction-diffusion system. The system describes the coexistence and interaction of water reservoirs, vegetation, and bushfire…
The question addressed here is the long time evolution of the solutions to a class of one-dimensional reaction-diffusion equations, in which the diffusion is given by an integral operator. The underlying motivation, discussed in the first…
We study the properties of Lotka-Volterra competitive models in which the intensity of the interaction among species depends on their position along an abstract niche space through a competition kernel. We show analytically and numerically…
We introduce a simplified technique for incorporating diffusive phenomena into lattice-gas molecular dynamics models. In this method, spatial interactions take place one dimension at a time, with a separate fractional timestep devoted to…
We consider a model for a population in a heterogeneous environment, with logistic type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior…
We investigate the Lotka-Volterra model for predator-prey competition with a finite carrying capacity that varies periodically in time, modeling seasonal variations in nutrients or food resources. In the absence of time variability, the…
Using statistical physics methods, we study generative diffusion models in the regime where the dimension of space and the number of data are large, and the score function has been trained optimally. Our analysis reveals three distinct…
In coupled reaction-diffusion systems, modes with two different length scales can interact to produce a wide variety of spatiotemporal patterns. Three-wave interactions between these modes can explain the occurrence of spatially complex…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
This paper studies the traveling wave solutions to a three species competition cooperation system. The existence of the traveling waves is investigated via monotone iteration method. The upper and lower solutions come from either the waves…
This chapter is a pedagogical review of methods and results for studying wave propagation in one-dimensional complex structures. We describe and compare the tight-binding, scattering matrix, transfer matrix and Riccati formalisms. We…