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A delayed, discrete-time, prey-predator model with Allee effects imposed on prey and predator populations is defined, and dynamics of the system is characterized computationally. The parametric conditions for local asymptotic stability of…

Populations and Evolution · Quantitative Biology 2021-07-27 Sujay Goldar , Sk. Sarif Hassan

The Fokker-Planck equation for the probability $f(r,t)$ to find a random walker at position $r$ at time $t$ is derived for the case that the the probability to make jumps depends nonlinearly on $f(r,t)$. The result is a generalized form of…

Statistical Mechanics · Physics 2008-08-20 James F. Lutsko , Jean Pierre Boon

We show that the occurrence of chaotic diffusion in a typical class of time-delayed systems with linear instantaneous and nonlinear delayed term can be well described by an anti-persistent random walk. We numerically investigate the…

Statistical Mechanics · Physics 2022-07-13 Tony Albers , David Müller-Bender , Günter Radons

We develop an analytical method to calculate encounter times of two random walkers in one dimension when each individual is segregated in its own spatial domain and shares with its neighbor only a fraction of the available space, finding…

Statistical Mechanics · Physics 2013-02-07 Luca Giuggioli , Sebastian Pérez-Becker , David P. Sanders

We consider a discrete-time random walk where the random increment at time step $t$ depends on the full history of the process. We calculate exactly the mean and variance of the position and discuss its dependence on the initial condition…

Statistical Mechanics · Physics 2009-11-10 Gunter M. Schütz , Steffen Trimper

We consider the one-dimensional partially asymmetric exclusion process with random hopping rates, in which a fraction of particles (or sites) have a preferential jumping direction against the global drift. In this case the accumulated…

Disordered Systems and Neural Networks · Physics 2009-11-10 R. Juhasz , L. Santen , F. Igloi

We consider a continuous-time random walk which is defined as an interpolation of a random walk on a point process on the real line. The distances between neighboring points of the point process are i.i.d. random variables in the normal…

Probability · Mathematics 2020-01-08 Alessandra Bianchi , Marco Lenci , Françoise Pène

Although the title seems self-contradictory, it does not contain a misprint. The model we study is a seemingly minor modification of the "true self-avoiding walk" (TSAW) model of Amit, Parisi, and Peliti in two dimensions. The walks in it…

Statistical Mechanics · Physics 2017-10-11 Peter Grassberger

Models for the behavior of ants and pedestrians are studied in an unified way in this paper. Each ant follows pheromone put by preceding ants, hence creating a trail on the ground, while pedestrians also try to follow others in a crowd for…

Statistical Mechanics · Physics 2009-11-13 Katsuhiro Nishinari , Ken Sugawara , Toshiya Kazama , Andreas Schadschneider , Debashish Chowdhury

In this paper, the dynamics of a modified Leslie-Gower predator-prey system with two delays and diffusion is considered. By calculating stability switching curves, the stability of positive equilibrium and the existence of Hopf bifurcation…

Dynamical Systems · Mathematics 2019-01-30 Yanfei Du , Ben Niu , Junjie Wei

We study a spatial (two-dimensional) Rosenzweig-MacArthur model under the following assumptions: $(1)$ prey movement follows a nonlinear diffusion, $(2)$ preys have a refuge zone (sometimes called "protection zone") where predators cannot…

Analysis of PDEs · Mathematics 2020-10-21 Leoncio Rodriguez Quinones , Jia Zhao , Luis Gordillo

Many ant species employ distributed population density estimation in applications ranging from quorum sensing [Pra05], to task allocation [Gor99], to appraisal of enemy colony strength [Ada90]. It has been shown that ants estimate density…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-06-08 Cameron Musco , Hsin-Hao Su , Nancy Lynch

Exploiting the coherent medium approximation, random walk among sites distributed randomly in space is investigated when the jump rate depends on the distance between two adjacent sites. In one dimension, it is shown that when the jump rate…

Statistical Mechanics · Physics 2021-09-27 Takashi Odagaki

The distribution of the first positive position reached by a random walker starting from the origin is fundamental for understanding the statistics of extremes and records in one-dimensional random walks. We present a comprehensive study of…

Statistical Mechanics · Physics 2025-09-03 Claude Godrèche , Jean-Marc Luck

We address prehensile pushing, the problem of manipulating a grasped object by pushing against the environment. Our solution is an efficient nonlinear trajectory optimization problem relaxed from an exact mixed integer non-linear trajectory…

Robotics · Computer Science 2025-03-19 Patrizio Perugini , Jens Lundell , Katharina Friedl , Danica Kragic

We identify a fundamental phenomenon of heterogeneous one dimensional random walks: the escape (traversal) time is maximized when the heterogeneity in transition probabilities forms a pyramid-like potential barrier. This barrier corresponds…

Probability · Mathematics 2020-07-29 Asaf Cassel , Shie Mannor , Guy Tennenholtz

We consider a spatially distributed population dynamics model with excitable predator-prey dynamics, where species propagate in space due to their taxis with respect to each other's gradient in addition to, or instead of, their diffusive…

Pattern Formation and Solitons · Physics 2009-11-10 V. N. Biktashev , J. Brindley , A. V. Holden , M. A. Tsyganov

The model of competition between densities of two different species, called predator and prey, is studied on a one dimensional periodic lattice, where each site can be in one of the four states say, empty, or occupied by a single predator,…

Statistical Mechanics · Physics 2011-06-02 Rakesh Chatterjee , P. K. Mohanty , Abhik Basu

We analyze a pair of diffusion equations which are derived in the infinite system--size limit from a microscopic, individual--based, stochastic model. Deviations from the conventional Fickian picture are found which ultimately relate to the…

Statistical Mechanics · Physics 2015-05-18 Duccio Fanelli , Alan J. McKane

We consider the elephant random walk with general step distribution. We calculate the first four moments of the limiting distribution of the position rescaled by $n^\alpha$ in the superdiffusive regime where $\alpha$ is the memory…

Probability · Mathematics 2022-10-03 József Kiss , Bálint Vető