Related papers: On Some Perturbation Approaches to Population Dyna…
Complex change is often described as "evolutionary" in economics, policy, and technology, yet most system dynamics models remain constrained to fixed state spaces and equilibrium-seeking behavior. This paper argues that evolutionary…
Dormancy is a costly adaptive strategy that is widespread among living organisms inhabiting diverse environments. We explore mathematical models of predator-prey systems, in order to assess the impact of prey dormancy on the competition…
Mathematical modeling and analysis of spatial-temporal population distributions of interacting species have gained significant attention in biology and ecology in recent times. In this work, we investigate a Bazykin-type prey-predator model…
In this paper, we show that different types of evolutionary game dynamics are, in principle, special cases of a dynamical system model based on our previously reported framework of generalized growth transforms. The framework shows that…
Attention mechanisms are widely used in artificial intelligence to enhance performance and interpretability. In this paper, we investigate their utility in modeling classical dynamical systems -- specifically, a noisy predator-prey…
Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy in a minimal ecosystem…
Predator-prey relationships are one of the most studied interactions in population ecology. However, little attention has been paid to the possibility of role exchange between species once determined as predators and preys, despite firm…
The recently developed method (Paper 1) enabling one to investigate the evolution of dynamical systems with an accuracy not dependent on time is developed further. The classes of dynamical systems which can be studied by that method are…
In the present work, we explore the influence of habitat complexity on the activities of prey and predator of a spatio-temporal system by incorporating self diffusion. First we modify the Rosenzweig-MacArthur predator-prey model by…
An impulsive model of augmentative biological control consisting of a general continuous predator-prey model in ordinary differential equations augmented by a discrete part describing periodic introductions of predators is considered. It is…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
We apply methods of dynamical systems to study the behaviour of the Randall-Sundrum models. We determine evolutionary paths for all possible initial conditions in a 2-dimensional phase space and we investigate the set of accelerated models.…
The computational complexity of time-dependent perturbation theory is well-known to be largely combinatorial whatever the chosen expansion method and family of parameters (combinatorial sequences, Goldstone and other Feynman-type…
Spatially extended population dynamics models that incorporate intrinsic noise serve as case studies for the role of fluctuations and correlations in biological systems. Including spatial structure and stochastic noise in predator-prey…
We deal with a Leslie-Gower predator-prey model with a generalist or alternating food for predator and linear functional response. Using a topological equivalent polynomial system we prove that the system is not Liouvillian (hence also not…
This work investigated the stability and asymptotic behavior of some Lotka Volterra type models. We used the Liapunov method which consists in analyzing the stability of systems of ordinary differential equations (ODEs) around the…
The commonly used accumulated payoff scheme is not invariant with respect to shifts of payoff values when applied locally in degree-inhomogeneous population structures. We propose a suitably modified payoff scheme and we show both formally…
Mathematical models of interacting populations are often constructed as systems of differential equations, which describe how populations change with time. Below we study one such model connected to the nonlinear dynamics of a system of…
A two-type two-sex branching process is introduced with the aim of describing the interaction of predator and prey populations with sexual reproduction and promiscuous mating. In each generation and in each species the total number of…
This paper is focused on local and global stability of a fractional-order predator-prey model with habitat complexity constructed in the Caputo sense and corresponding discrete fractional-order system. Mathematical results like positivity…