相关论文: Fixation in a cyclic Lotka-Volterra model
In this work we consider three species competing with each other in the same habitat. One of the species lives in the entire habitat, competing with the other two species, while the other two inhabit two disjoint regions of the habitat.…
For special $d$-dimensional hyperbolic shells $E$ with $ d\geq 5$ we show that the number of lattice points in $E$ intersected with a $d$-dimensional cube $C_r$ of edge length $r$, can be approximated by the volume of $E\cap C_r$, as $r$…
A simple d-dimensional lattice model is proposed, incorporating some degree of frustration and thus capable of describing some aspects of molecular orientation in covalently bound molecular solids. For d=2 the model is shown to be…
The isotropic-nematic (I-N) phase transition in a system of long straight rigid rods of length k on square lattices is studied by combining Monte Carlo simulations and theoretical analysis. The process is analyzed by comparing the…
There is a finite number $h_{n,d}$ of tight frames of $n$ distinct vectors for $\mathbb{C}^d$ which are the orbit of a vector under a unitary action of the cyclic group $\mathbb{Z}_n$. These cyclic harmonic frames (or geometrically uniform…
A system of nonlinear ordinary differential equations with forcing function is developed to model evolution processes in complex systems. In this system R, C, and P are the resource, consumption, and production functions correspondingly. F…
We study a simple dynamical model exhibiting sequential dynamics. We show that in this model there exist sets of parameter values for which a cyclic chain of saddle equilibria, $O_k$, $k=1, \ldots, p$, have two dimensional unstable…
We study the spreading of families in two-dimensional multispecies predator-prey systems, in which species cyclically dominate each other. In each time step randomly chosen individuals invade one of the nearest sites of the square lattice…
The site and bond percolation problems are conventionally studied on (hyper)cubic lattices, which afford straightforward numerical treatments. The recent implementation of efficient simulation algorithms for high-dimensional systems now…
We consider a class of continuous-time stochastic growth models on $d$-dimensional lattice with non-negative real numbers as possible values per site. We remark that the diffusive scaling limit proven in our previous work [Nagahata, Y.,…
The work contains a detailed study of the scaling limit of a certain critical, integrable inhomogeneous six-vertex model subject to twisted boundary conditions. It is based on a numerical analysis of the Bethe ansatz equations as well as…
A flat of a matroid is cyclic if it is a union of circuits. The cyclic flats of a matroid form a lattice under inclusion. We study these lattices and explore matroids from the perspective of cyclic flats. In particular, we show that every…
In this article we report a preliminary investigation of the large $N$ limit of a generalized one-matrix model which represents an $O(n)$ symmetric model on a random lattice. The model on a regular lattice is known to be critical only for…
Dynamical systems are a valuable asset for the study of population dynamics. On this topic, much has been done since Lotka and Volterra presented the very first continuous system to understand how the interaction between two species -- the…
We consider cyclic Lotka-Volterra models with three and four strategies where at every interaction agents play a strategy using a time-dependent probability distribution. Agents learn from a loss by reducing the probability to play a losing…
We analyze the nonlinear relaxation of a complex ecosystem composed of many interacting species. The ecological system is described by generalized Lotka-Volterra equations with a multiplicative noise. The transient dynamics is studied in…
We study a d-dimensional lattice model of diffusing coalescing massive particles, with two parameters controlling deposition and evaporation of monomers. The unique stationary distribution for the system exhibits a phase transition in all…
In this paper, we are concerned with the permanence of a Lotka-Volterra model of three competing species with seasonal succession. Based on the existence of a carrying simplex, that is a globally attracting hypersurface of codimension one,…
I define lattice fermions in five Euclidean dimensions and the corresponding effective theory in four dimensions. The main properties of these theories include the suppression of high momentum modes of the lattice Dirac operator and their…
We consider random dynamical systems generated by a special class of Volterra quadratic stochastic operators on the simplex $S^{m-1}$. We prove that in contrast to the deterministic set-up the trajectories of the random dynamical system…