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We analyze the asymptotic behavior of sequences of random variables defined by an initial condition, a stationary and ergodic sequence of random matrices, and an induction formula involving multiplication is the so-called max-plus algebra.…
In this paper we consider a class of discrete time prey-predator models with three interacting species defined on the two-dimensional simplex. For some choices of parameters of the operator describing the evolution of the relative…
In the theory of cellular automata, an oscillator is a pattern that repeats itself after a fixed number of generations; that number is called its period. A cellular automaton is called omniperiodic if there exist oscillators of all periods.…
A new mechanism is proposed to explain the appearance of the three known fermion generations in a natural way. The underlying idea is based on the discreteness of the spectrum of solutions of the gap equation appearing in models of…
In this letter, we investigate the population dynamics in a May-Leonard formulation of the rock-paper-scissors game in which one or two species, which we shall refer to as "weak", have a reduced predation or reproduction probability. We…
When an oscillator switches abruptly between different frequencies, there is some ambiguity in deciding how the system should be modelled at the switch. Here we describe two seemingly natural models of a switch in a simple…
It is known that there are no more Lyndon words of length n than there are periodic necklaces of same length. This paper considers a similar problem where, additionally, the necklaces must be without some forbidden factors. This problem…
We study a stochastic lattice predator-prey system by means of Monte Carlo simulations that do not impose any restrictions on the number of particles per site, and discuss the similarities and differences of our results with those obtained…
The monarch butterfly annually migrates from central Mexico to southern Canada. During recent decades, its population has been reduced due to human interaction with their habitat. We examine the effect of herbicide usage on the monarch…
A fundamental issue discussed in evolutionary biology is the transition from unicellular to multicellular organisms. Here we develop non-robust models provided in [1] and attempt to get robust models investigated how differentiation of…
We study the dynamics of a second-order difference equation that is derived from a planar Ricker model of two-stage (e.g. adult, juvenile) biological populations. We obtain sufficient conditions for global convergence to zero in the…
The reproduction of a living cell requires a repeatable set of chemical events to be properly coordinated. Such events define a replication cycle, coupling the growth and shape change of the cell membrane with internal metabolic reactions.…
Multiple scales in metapopulations can give rise to paradoxical behaviour: in a conceptual model for a public goods game, the species associated with a fitness cost due to the public good production can be stabilised in the well-mixed limit…
Using as a narrative theme the example of Darwin's finches, a microscopic agent-based model is introduces to study sympatric speciation as a result of competition for resources in the same ecological niche. Varying competition among…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
We consider the model checking problem of infinite state systems given in the form of parameterized discrete timed networks with multiple clocks. We show that this problem is decidable with respect to specifications given by B- or…
We investigate one-dimensional elementary probabilistic cellular automata (PCA) whose dynamics in first-order mean-field approximation yields discrete logisticlike growth models for a single-species unstructured population with…
Dynamic exploration for a predator-prey bio-system of two species with ratio-dependent functional response is carried out, where the capability to predate in both the stages of the predator, the juvenile and the matured, is taken into…
An explanatory model for the emergence of evolvable units must display emerging structures that (1) preserve themselves in time (2) self-reproduce and (3) tolerate a certain amount of variation when reproducing. To tackle this challenge,…
A deterministic finite (semi)automaton is primitive if its transition monoid (semigroup) acting on the set of states has no non-trivial congruences. It is synchronizing if it contains a constant map (transformation). In analogy to…