arXiv subjects

Matti Peltomaki

Publications and source records attributed to Matti Peltomaki.

5 recordsLinked to original sources

arXiv2009

Characterizing spatiotemporal patterns in three-state lattice models

A two-species spatially extended system of hosts and parasitoids is studied. There are two distinct kinds of coexistence; one with populations distributed homogeneously in space and another one with spatiotemporal patterns. In the latter case, there are noise-sustained oscillations in the population densities, whereas in the former one the densities are essentially constants in time with small fluctuations. We introduce several metrics to characterize the patterns and onset thereof. We also build a consistent sequence of corrections to the mean-field equations using a posteriori knowledge from simulations. These corrections both lead to better description of the dynamics and connect the patterns to it. The analysis is readily applicable to realistic systems, which we demonstrate by an example using an empirical metapopulation landscape.

q-bio.PE↗

arXiv2008

Oscillations and patterns in interacting populations of two species

Interacting populations often create complicated spatiotemporal behavior, and understanding it is a basic problem in the dynamics of spatial systems. We study the two-species case by simulations of a host--parasitoid model. In the case of co-existence, there are spatial patterns leading to noise-sustained oscillations. We introduce a new measure for the patterns, and explain the oscillations as a consequence of a timescale separation and noise. They are linked together with the patterns by letting the spreading rates depend on instantaneous population densities. Applications are discussed.

q-bio.PE↗

arXiv2008

Three- and four-state rock-paper-scissors games with diffusion

Cyclic dominance of three species is a commonly occurring interaction dynamics, often denoted the rock-paper-scissors (RPS) game. Such type of interactions is known to promote species coexistence. Here, we generalize recent results of Reichenbach et al. (e.g. Nature 448, 1046 (2007)) of a four-state variant of RPS. We show that spiral formation takes place only without a conservation law for the total density. Nevertheless, in general fast diffusion can destroy species coexistence. We also generalize the four-state model to slightly varying reaction rates. This is shown both analytically and numerically not to change pattern formation, or the effective wave length of the spirals, and therefore does not alter the qualitative properties of the cross-over to extinction.

q-bio.PE↗

arXiv2005

Correlations in Bipartite Collaboration Networks

Collaboration networks are studied as an example of growing bipartite networks. These have been previously observed to have structure such as positive correlations between nearest-neighbour degrees. However, a detailed understanding of the origin of this phenomenon and the growth dynamics is lacking. Both of these are analyzed empirically and simulated using various models. A new one is presented, incorporating empirically necessary ingredients such as bipartiteness and sublinear preferential attachment. This, and a recently proposed model of team assembly both agree roughly with some empirical observations and fail in several others.

physics.soc-ph↗

arXiv2005

Host--parasite models on graphs

The behavior of two interacting populations, ``hosts''and ``parasites'', is investigated on Cayley trees and scale-free networks. In the former case analytical and numerical arguments elucidate a phase diagram, whose most interesting feature is the absence of a tri-critical point as a function of the two independent spreading parameters. For scale-free graphs, the parasite population can be described effectively by Susceptible-Infected-Susceptible-type dynamics in a host background. This is shown both by considering the appropriate dynamical equations and by numerical simulations on Barabási-Albert networks with the major implication that in the termodynamic limit the critical parasite spreading parameter vanishes.

cond-mat.stat-mech↗