ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


Population dynamics

Hybrid SIRS model of infection spread

Purpose of this work is to build a model of the infection spread in the form of a system of differential equations that takes into account the inertial nature of the transfer of infection between individuals. Methods. The paper presents a theoretical and numerical study of the structure of the phase space of the system of ordinary differential equations of the mean field model. Results. A modified SIRS model of epidemic spread is constructed in the form of a system of ordinary differential equations of the third order.

Synchronization of infections spread processes in populations interacting: Modeling by lattices of cellular automata

Purpose. Study of synchronization of oscillations in ensembles of probabilistic cellular automata that simulate the spread of infections in biological populations. Method. Numerical simulation of the square lattice of cellular automata by means of the Monte Carlo method, investigation of synchronization of oscillations by time-series analisys and by the coherence function. Results. The effect has been found of synchronization of irregular oscillations, similar to the phenomenon of synchronization of chaos in dynamical systems.

SIRS-model with dynamic regulation of the population: Probabilistic cellular automata approach

Aim. Construction a model of infection spread in the form of a lattice of stochastic cellular automata which can demonstrate nontrivial oscillating regimes; investigation of its dynamics and comparison with the mean-field model. Method. Numerical simulation of the square lattice of cellular automata by the Monte Carlo approach, theoretical and numerical study of the structure of the phase space of its mean-field model. Results. A modified SIRS-model of epidemic propagation has been proposed in the form of a lattice of stochastic cellular automata.

Bifurcations in active predator – passive prey model

Bifurcations were studied numerically in the system of partial differential equations, which is  a one variant of predator-prey models. The mathematical model takes into account spatial  distribution in habitat, active directed predator movements, birth and death process in prey  population. The analysis of possible population dynamics development was performed by two  qualitatively different discrete sampling techniques (Bubnov–Galerkin’s method and grid method).

Stochastic sensitivity of limit cycles for «predator – two preys» model

We consider the population dynamics model «predator – two preys». A deterministic stability of limit cycles of this three-dimensional model in a period doubling bifurcations zone at the transition from an order to chaos is investigated. Stochastic sensitivity of cycles for additive and parametrical random disturbances is analyzed with the help of stochastic sensitivity function technique. Thin effects of stochastic influences are demonstrated. Growth of stochastic sensitivity of cycles for period doubling under transition from order to chaos is shown.

Synchronizing the period-­2 cycle in the system of symmetrical coupled populations with stock–recruitment based on the Ricker population model

We investigated coupled map lattices based on the Ricker model that describes the spatial dynamics of heterogeneous populations represented by two connected groups of individuals with a migration interaction between them. Bifurcation mechanisms in­phase and antiphase synchronization of multistability regimes were considered in such systems. To identify a synchronization mode we introduced the quantitative measure of synchronization.

Analysis of attractors for stochastically forced «predator–prey» model

We consider the population dynamics model «predator–prey». Equilibria and limit cycles of system are studied from both deterministic and stochastic points of view. Probabilistic properties of stochastic trajectories are investigated on the base of stochastic sensitivity function technique. The possibilities of stochastic sensitivity function to analyse details and thin features of stochastic attractors are demonstrated.