相关论文: Flocking Regimes in a Simple Lattice Model
May and Leonard (SIAM J. Appl. Math 1975) introduced a three-species Lotka-Volterra type population model that exhibits heteroclinic cycling. Rather than producing a periodic limit cycle, the trajectory takes longer and longer to complete…
We study a stochastic model of collective motion in which individuals update their orientation through pairwise aligning or anti-aligning copying interactions. We analyze both annealed dynamics, where interaction types are chosen…
In this paper a geometric field theory of dislocation dynamics and finite plasticity in single crystals is formulated. Starting from the multiplicative decomposition of the deformation gradient into elastic and plastic parts, we use…
Off-equilibrium dynamics of a three-dimensional lattice model with nearest- and next nearest-neighbors exclusions is studied. At equilibrium, the model undergoes a first-order fluid-solid transition. Non-equilibrium filling, through random…
In this paper, we propose a numerical investigation of topological interactions in flocking dynamics. Starting from a microscopic description of the phenomena, mesoscopic and macroscopic models have been previously derived under specific…
We study the lattice random walk dynamics in a heterogeneous space of two media separated by an interface and having different diffusivity and bias. Depending on the position of the interface, there exist two exclusive ways to model the…
We present a method enabling a large number of agents to learn how to flock, which is a natural behavior observed in large populations of animals. This problem has drawn a lot of interest but requires many structural assumptions and is…
We study the effects of animal social networks with a weighted pattern of interactions on the flocking transition exhibited by models of self-organized collective motion. Considering a model representing dynamics on a one-dimensional…
A simple model is presented to investigate an impact of the double occupied sites on the ground state energy of a lattice. The model is seen as a useful tool to introduce undergraduate or graduate physics students to an array of a…
Birds in a flock move in a correlated way, resulting in large polarization of velocities. A good understanding of this collective behavior exists for linear motion of the flock. Yet observing actual birds, the center of mass of the group…
We compute the growth fluctuations in equilibrium of a wide class of deposition models. These models also serve as general frame to several nearest-neighbor particle jump processes, e.g. the simple exclusion or the zero range process, where…
I study a population model in which the reproduction rate lambda is inherited with mutation, favoring fast reproducers in the short term, but conflicting with a process that eliminates agglomerations of individuals. The model is a variant…
A one-dimensional flocking model using active Ising spins is studied, where the system evolves through the reinforcement learning approach \textit{via} defining state, action, and cost function for each spin. The orientation of spin with…
We study the dynamics of the generalized Lotka-Volterra model with a network structure. Performing a high connectivity expansion for graphs, we write down a mean-field dynamical theory that incorporates degree heterogeneity. This allows us…
The requisites for the persistence of small colonies of self-replicating molecules living in a two-dimensional lattice are investigated analytically in the infinite diffusion or mean-field limit and through Monte Carlo simulations in the…
Many animal groups are heterogeneous and may even consist of individuals of different species, called mixed-species flocks. Mathematical and computational models of collective animal movement behaviour, however, typically assume that groups…
Multidimensional systems coupled via complex networks are widespread in nature and thus frequently invoked for a large plethora of interesting applications. From ecology to physics, individual entities in mutual interactions are grouped in…
The self- and mutual-avoiding walk used in conventional lattice models for polymeric systems requires that all lattice sites, polymer segments, and solvent molecules (unoccupied lattice sites) have the same volume. This incorrectly accounts…
We present studies for an individual based model of three interacting populations whose individuals are mobile in a 2D-lattice. We focus on the pattern formation in the spatial distributions of the populations. Also relevant is the…
A microscopic approach to macroeconomic features is intended. A model for macroeconomic behavior under heterogeneous spatial economic conditions is reviewed. A birth-death lattice gas model taking into account the influence of an economic…