Related papers: Competitive Brownian and Levy walkers
This paper enhances the classical Solow model of economic growth by integrating L\'evy noise, a type of non-Gaussian stochastic perturbation, to capture the inherent uncertainties in economic systems. The extended model examines the impact…
Bacteria regulate their motility through a variety of mechanisms, including quorum sensing (QS) and other density-dependent responses mediated by diffusible signals. While nonlinear density-dependent motility is well known in active-matter…
This chapter investigates some mechanisms behind pattern formation driven by competitive-only or repelling interactions, and explores how these patterns are influenced by different types of particle movement. Despite competition and…
We study the influence of a dissipation process on diffusion dynamics triggered by slow fluctuations. We study both strong- and weak-friction regime. When the latter regime applies, the system is attracted by the basin of either Gauss or…
The dynamics of dispersal-structured populations, consisting of competing individuals that are characterized by different diffusion coefficients but are otherwise identical, is investigated. Competition is taken into account through…
Interactions among living organisms, from bacteria colonies to human societies, are inherently more complex than interactions among particles and nonliving matter. Group interactions are a particularly important and widespread class,…
The standard diffusive spreading, characterized by a Gaussian distribution with mean square displacement that grows linearly with time, can break down, for instance, under the presence of correlations and heterogeneity. In this work, we…
L\'evy flights represent the best strategy to randomly search for a target in an unknown environment, and have been widely observed in many animal species. Here, we inspect and discuss recent results concerning human behavior and cognition.…
Scale-invariant spatial or temporal patterns and L\'evy flight motion have been observed in a large variety of biological systems. It has been argued that animals in general might perform L\'evy flight motion with power law distribution of…
The L\'evy, jumping process, defined in terms of the jumping size distribution and the waiting time distribution, is considered. The jumping rate depends on the process value. The fractional diffusion equation, which contains the variable…
This paper investigates L\'evy walks with random velocities, extending classical models beyond constant speed assumptions. We derive scaling limits, demonstrating that diffusion depends on interplay between heavy-tailed duration and…
The evolution of dispersal rate is studied with a model of several local populations linked by dispersal. Three dispersal strategies are considered where all, half, or none of the offspring disperse. The spatial scale (number of patches)…
Resource competition is a fundamental interaction in natural communities.However little is known about competition in spatial environments where organisms are able to regulate resource distributions. Here, we analyze the competition of two…
A discrete-time model of reacting evolving fields, transported by a bidimensional chaotic fluid flow, is studied. Our approach is based on the use of a Lagrangian scheme where {\it fluid particles} are advected by a $2d$ symplectic map…
Transport of the Brownian particles driven by L\'evy flights coexisting with subdiffusion in asymmetric periodic potentials is investigated in the absence of any external driving forces. Using the Langevin-type dynamics with subordination…
We study a system of self-propelled, proliferating finite-size disks with game-theoretical interactions, where growth rates depend on local population composition. We analyze how these interactions influence spatial distribution,…
Population-level scaling in ecological systems arises from individual growth and death with competitive constraints. We build on a minimal dynamical model of metabolic growth where the tension between individual growth and mortality…
Flocking is a paradigmatic example of collective animal behaviour, where decentralized interaction rules give rise to a globally ordered state. In the emergence of order out of self-organization we find similarities between biological…
Compared to the well-studied topic of human mobility in real geographic space, very few studies focus on human mobility in virtual space, such as interests, knowledge, ideas, and so forth. However, it relates to the issues of management of…
The temporal dynamics of social interactions were shown to influence the spread of disease. Here, we model the conditions of progression and competition for several viral strains, exploring various levels of cross-immunity over temporal…