arXiv subjects

Mohamed Swailem

Publications and source records attributed to Mohamed Swailem.

6 recordsLinked to original sources

arXiv2026

Parametric resonance, chaos and spatial structure in the Lotka-Volterra model

We investigate the Lotka-Volterra model for predator-prey competition with a finite carrying capacity that varies periodically in time, modeling seasonal variations in nutrients or food resources. In the absence of time variability, the ordinary differential equations have an equilibrium point that represents coexisting predators and prey. The time dependence removes this equilibrium solution, but the equilibrium point is restored by allowing the predation rate also to vary in time. This equilibrium can undergo a parametric resonance instability, leading to subharmonic and harmonic time-periodic behavior, which persists even when the predation rate is constant. We also find period-doubling bifurcations and chaotic dynamics. If we allow the population densities to vary in space as well as time, introducing diffusion into the model, we find that variations in space diffuse away when the underlying dynamics is periodic in time, but spatiotemporal structure persists when the underlying dynamics is chaotic. We interpret this as a competition between diffusion, which makes the population densities homogeneous in space, and chaos, where sensitive dependence on initial conditions leads to different locations in space following different trajectories in time. Patterns and spatial structure are known to enhance resilience in ecosystems, suggesting that chaotic time-dependent dynamics arising from seasonal variations in carrying capacity and leading to spatial structure, might also enhance resilience.

nlin.PS↗

arXiv2025

Fixation and extinction in time-fluctuating spatially structured metapopulations

Bacteria evolve in volatile environments and complex spatial structures. Migration, fluctuations and environmental variability therefore have a significant impact on the evolution of microbial populations. Here, we consider a class of spatially explicit metapopulation models arranged as regular (circulation) graphs where wild-type and mutant cells compete in a time-fluctuating environment in which demes (subpopulations) are connected by slow cell migration. The carrying capacity is the same at each deme and endlessly switches between two values associated to harsh and mild environmental conditions. Environmental variability can lead to population bottlenecks, following which the population is prone to fluctuation-induced extinction. Here, we analyse how slow migration, spatial structure, and fluctuations affect the phenomena of fixation and extinction on clique, cycle, and square lattice metapopulations. When the carrying capacity remains large, bottlenecks are weak and deme extinction can be ignored. The dynamics is thus captured by a coarse-grained description within which the probability and mean time of fixation are obtained analytically. This allows us to show that, in contrast to static environments, the mutant fixation probability depends on the rate of migration. We also show that the fixation probability and mean fixation time can exhibit a non-monotonic dependence on the switching rate. When the carrying capacity is small under harsh conditions, bottlenecks are strong, and the metapopulation evolution is shaped by the coupling of deme extinction and strain competition. This yields rich dynamical scenarios, among which we identify the best conditions to eradicate mutants without dooming the metapopulation to extinction. We offer an interpretation of these findings in the context of an idealised treatment strategy and discuss possible generalisations of our models.

q-bio.PE↗

arXiv2025

Agent-based Monte Carlo simulations for reaction-diffusion models, population dynamics, and epidemic spreading

We provide an overview of Monte Carlo algorithms based on Markovian stochastic dynamics of interacting and reacting many-particle systems not in thermal equilibrium. These agent-based simulations are an effective way of introducing students to current research without requiring much prior knowledge or experience. By starting from the direct visualization of the data, students can gain immediate insight into emerging macroscopic features of a complex system and subsequently apply more sophisticated data analysis to quantitatively characterize its rich dynamical properties, both in the stationary and transient regimes. We utilize simulations of reaction-diffusion systems, stochastic models for population dynamics and epidemic spreading, to exemplify how interdisciplinary computational research can be effectively utilized in bottom-up undergraduate and graduate education through learning by doing. We also give helpful hints for the practical implementation of Monte Carlo algorithms, provide sample codes, explain some typical data analysis tools, and describe various potential error sources and pitfalls and tips for avoiding them.

cond-mat.stat-mech↗

arXiv2024

Computing macroscopic reaction rates in reaction-diffusion systems using Monte Carlo simulations

Stochastic reaction-diffusion models are employed to represent many complex physical, biological, societal, and ecological systems. The macroscopic reaction rates describing the large-scale kinetics in such systems are effective, scale-dependent parameters that need to be either measured experimentally or computed using a microscopic model. In a Monte Carlo simulation of stochastic reaction-diffusion systems, microscopic probabilities for specific events to happen serve as the input control parameters. Finding the functional dependence of emergent macroscopic rates on the microscopic probabilities is a difficult problem, and there is no systematic analytical way to achieve this goal. Therefore, we introduce a straightforward numerical method of using Monte Carlo simulations to evaluate the macroscopic reaction rates by directly obtaining the count statistics of how many events occur per simulation time step. Our technique is first tested on well-understood fundamental examples, namely restricted birth processes, diffusion-limited two-particle coagulation, and two-species pair annihilation kinetics. Next we utilize the thus gained experience to investigate how the microscopic algorithmic probabilities become coarse-grained into effective macroscopic rates in more complex model systems such as the Lotka--Volterra model for predator-prey competition and coexistence, as well as the rock-paper-scissors or cyclic Lotka--Volterra model as well as its May--Leonard variant that capture population dynamics with cyclic dominance motifs. Thereby we achieve a deeper understanding of coarse-graining in spatially extended stochastic reaction systems and the nontrivial relationships between the associated microscopic and macroscopic model parameters. The proposed technique should generally provide a useful means to better fit Monte Carlo simulation results to experimental or observational data.

physics.bio-ph↗

arXiv2023

Lotka-Volterra predator-prey model with periodically varying carrying capacity

We study the stochastic spatial Lotka-Volterra (LV) model for predator-prey interaction subject to a periodically varying carrying capacity. The LV model with on-site lattice occupation restrictions that represent finite food resources for the prey exhibits a continuous active-to-absorbing phase transition. The active phase is sustained by spatio-temporal patterns in the form of pursuit and evasion waves. Monte Carlo simulations on a two-dimensional lattice are utilized to investigate the effect of seasonal variations of the environment on species coexistence. The results of our simulations are also compared to a mean-field analysis. We find that the parameter region of predator and prey coexistence is enlarged relative to the stationary situation when the carrying capacity varies periodically. The stationary regime of our periodically varying LV system shows qualitative agreement between the stochastic model and the mean-field approximation. However, under periodic carrying capacity switching environments, the mean-field rate equations predict period-doubling scenarios that are washed out by internal reaction noise in the stochastic lattice model. Utilizing visual representations of the lattice simulations and dynamical correlation functions, we study how the pursuit and evasion waves are affected by ensuing resonance effects. Correlation function measurements indicate a time delay in the response of the system to sudden changes in the environment. Resonance features are observed in our simulations that cause prolonged persistent spatial correlations. Different effective static environments are explored in the extreme limits of fast- and slow periodic switching. The analysis of the mean-field equations in the fast-switching regime enables a semi-quantitative description of the stationary state.

q-bio.PE↗

arXiv2023

Perturbative Field-Theoretical Analysis of Three-Species Cyclic Predator-Prey Models

We apply a perturbative Doi--Peliti field-theoretical analysis to the stochastic spatially extended symmetric Rock-Paper-Scissors (RPS) and May--Leonard (ML) models, in which three species compete cyclically. Compared to the two-species Lotka--Volterra predator-prey (LV) model, according to numerical simulations, these cyclical models appear to be less affected by intrinsic stochastic fluctuations. Indeed, we demonstrate that the qualitative features of the ML model are insensitive to intrinsic reaction noise. In contrast, and although not yet observed in numerical simulations, we find that the RPS model acquires significant fluctuation-induced renormalizations in the perturbative regime, similar to the LV model. We also study the formation of spatio-temporal structures in the framework of stability analysis and provide a clearcut explanation for the absence of spatial patterns in the RPS system, whereas the spontaneous emergence of spatio-temporal structures features prominently in the LV and the ML models.

cond-mat.stat-mech↗