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The inner structure of the attractor appearing when the Varley-Gradwell-Hassell population model bifurcates from regular to chaotic behaviour is studied. By algebraic and geometric arguments the coexistence of a continuum of neutrally…
Circadian rhythms are acquired through evolution to increase the chances for survival through synchronizing with the daylight cycle. Reliable synchronization is realized through two trade-off properties: regularity to keep time precisely,…
We introduce a one-parameter family of polymatrix replicators defined in a three-dimensional cube and study its bifurcations. For a given interval of parameters, this family exhibits suspended horseshoes and persistent strange attractors.…
Timed automata are a convenient mathematical model for modelling and reasoning about real-time systems. While they provide a powerful way of representing timing aspects of such systems, timed automata assume arbitrary precision and…
Including spatial structure and stochastic noise invalidates the classical Lotka-Volterra picture of stable regular population cycles emerging in models for predator-prey interactions. Growth-limiting terms for the prey induce a continuous…
Periodic dynamical systems, distinguished by their repetitive behavior over time, are prevalent across various engineering disciplines. In numerous applications, particularly within industrial contexts, the implementation of model…
Periodic patterns in dynamical behaviours of biological models described by simple form differential delay equations are studied. Mathematical models are given by a class of scalar delay differential equations with a multiplicative time…
We study the spatial rock-paper-scissors model, where resource competitors' cyclic dominance impacts organisms' energy levels. Our model assumes that failed selection interactions can lead to energy loss, reducing the chances of success in…
The main purpose of this paper is to study the existence of periodic solutions for a nonautonomous differential-difference system describing the dynamics of hematopoietic stem cell (HSC) population under some external periodic regulatory…
We develop the qualitative theory of the solutions of the McKendrick partial differential equation of population dynamics. We calculate explicitly the weak solutions of the McKendrick equation and of the Lotka renewal integral equation with…
We propose a generic model of eco-systems, with a {\it hierarchical} food web structure. In our computer simulations we let the eco-system evolve continuously for so long that that we can monitor extinctions as well as speciations over…
In this paper we explain the biophysical principles which, according to us, govern the Proteus mirabilis swarm phenomenon. Then, we translate this explanation into a mathematical model, essentially based on partial differential equations.…
We address the existence of periodic orbits for periodic eco-epidemiological system with disease in the prey. To do it, we consider three main steps. Firstly we study a one parameter family of systems and obtain uniform bounds for the…
We present numerical results based on a simplified ecological system in evolution, showing features of extinction similar to that claimed for the biosystem on Earth. In the model each species consists of a population in interaction with the…
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 adopt a physically motivated empirical approach to the characterisation of the distributions of twin and triplet primes within the set of primes, rather than in the set of all natural numbers. Remarkably, the occurrences of twins or…
A mathematical model to describe period-memorizing behavior in Physarum plasmodium are reported. In constructing the model, we first examine the basic characteristics required for the class of models, then create a minimal linear model to…
Identifying and quantifying the benefits of sex and recombination is a long standing problem in evolutionary theory. In particular, contradictory claims have been made about the existence of a benefit of recombination on high dimensional…
Paradoxes that can supposedly occur if a time machine is created are discussed. It is shown that the existence of trajectories of ``multiplicity zero'' (i.e. trajectories that describe a ball hitting its younger self so that the latter…
This article is interested in the origin of the genetic code, it puts forward a scenario of a simultaneous selection of the bases and amino acids and setting up of a correlation between them. Each amino acid is associated with a pair of its…