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    Wyświetlanie 1-4 z 4
    Tytuł:
    Stability and Hopf bifurcation analysis for a Lotka-Volterra predator-prey model with two delays
    Autorzy:
    Xu, C.
    Liao, M.
    He, X.
    Powiązania:
    https://bibliotekanauki.pl/articles/907822.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    opóźnienie
    stabilność
    bifurkacja Hopfa
    predator-prey model
    delay
    stability
    Hopf bifurcation
    Opis:
    In this paper, a two-species Lotka-Volterra predator-prey model with two delays is considered. By analyzing the associated characteristic transcendental equation, the linear stability of the positive equilibrium is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and direction of Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using normal form theory and center manifold theory. Some numerical simulations for supporting the theoretical results are also included.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2011, 21, 1; 97-107
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Dynamic stability and spatial heterogeneity in the individual-based modelling of a Lotka-Volterra gas
    Autorzy:
    Waniewski, J.
    Jędruch, W.
    Żołek, N. S.
    Powiązania:
    https://bibliotekanauki.pl/articles/907374.pdf
    Data publikacji:
    2004
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    równanie Lotka-Volterra
    entropia
    współczynnik korelacji
    predator-prey system
    entropy
    correlation coefficient
    Opis:
    Computer simulation of a few thousands of particles moving (approximately) according to the energy and momentum conservation laws on a tessellation of 800 x 800 squares in discrete time steps and interacting according to the predator-prey scheme is analyzed. The population dynamics are described by the basic Lotka-Volterra interactions (multiplication of preys, predation and multiplication of predators, death of predators), but the spatial effects result in differences between the system evolution and the mathematical description by the Lotka-Volterra equations. The spatial patterns were evaluated using entropy and a cross correlation coefficient for the spatial distribution of both populations. In some simulations the system oscillated with variable amplitude but rather stable period, but the particle distribution departed from the (quasi) homogeneous state and did not return to it. The distribution entropy oscillated in the same rhythm as the population, but its value was smaller than in the initial homogeneous state. The cross correlation coefficient oscillated between positive and negative values. Its average value depended on the space scale applied for its evaluation with the negative values on the small scale (separation of preys from predators) and the positive values on the large scale (aggregation of both populations). The stability of such oscillation patterns was based on a balance of the population parameters and particle mobility. The increased mobility (particle mixing) resulted in unstable oscillations with high amplitude, sustained homogeneity of the particle distribution, and final extinction of one or both populations.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2004, 14, 2; 139-147
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Spatial Heterogeneity and Local Oscillation Phase Drifts Individual-Based Simulations of a Prey-Predator System
    Autorzy:
    Waniewski, J.
    Jędruch, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/929763.pdf
    Data publikacji:
    2000
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    estymacja parametryczna
    różnorodność przestrzenna
    prey-predator system
    individual-based simulations
    spatial heterogeneity
    oscillation phase drift
    parameter estimation
    Opis:
    Individual-based simulations of a simple prey-predator system of Lotka-Volterra type were carried out on a tessellation of identical squares with discrete time steps. The particles representing individuals moved freely along (roughly) straight lines with constant (on the average) velocity, and changed their movement during a collision with another particle. Individuals were of two types: preys (with free exponential population growth) and predators (with exponential population decrease in the absence of a prey, they attack with probability one and are characterized by zero handling and gestationtimes). Therefore the system might be also interpreted as a chemical reactionin a gas. For this simple system, a spontaneous generation of complex spatio-temporal pattern was observed with wavy spatial patterns and tendency for preys to form clusters surrounded by predators if the population density was high. The oscillations of the system were investigated at different spatial scales, and the phase lag between the oscillations in different local observation windows was demonstrated. The parameters of the classical Lotka-Volterra equations were estimated and the impact of the migration and the oscillation phase drift on the parameter values was discussed.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2000, 10, 1; 175-192
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Bifurcation and control for a discrete-time prey–predator model with Holling-IV functional response
    Autorzy:
    Chen, Q.
    Teng, Z.
    Hu, Z.
    Powiązania:
    https://bibliotekanauki.pl/articles/907649.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    discrete prey predator model
    flip bifurcation
    Hopf bifurcation
    saddle node bifurcation
    OGY chaotic control
    bifurkacja Hopfa
    sterowanie chaosem
    Opis:
    The dynamics of a discrete-time predator–prey model with Holling-IV functional response are investigated. It is shown that the model undergoes a flip bifurcation, a Hopf bifurcation and a saddle-node bifurcation by using the center manifold theorem and bifurcation theory. Numerical simulations not only exhibit our results with the theoretical analysis, but also show the complex dynamical behaviors, such as the period-3, 6, 9, 12, 20, 63, 70, 112 orbits, a cascade of period-doubling bifurcations in period-2, 4, 8, 16, quasi-periodic orbits, an attracting invariant circle, an inverse period-doubling bifurcation from the period-32 orbit leading to chaos and a boundary crisis, a sudden onset of chaos and a sudden disappearance of the chaotic dynamics, attracting chaotic sets and non-attracting sets. We also observe that when the prey is in chaotic dynamics the predator can tend to extinction or to a stable equilibrium. Specifically, we stabilize the chaotic orbits at an unstable fixed point by using OGY chaotic control.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2013, 23, 2; 247-261
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-4 z 4

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