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In this paper, we investigate a discrete-time prey-predator model. The model is formulated by using the piecewise constant argument method for differential equations and taking into account Holling type III. The existence and local behavior of equilibria are studied. We established that the system experienced both Neimark-Sacker and perioddoubling bifurcations analytically by using bifurcation theory and the center manifold theorem. In order to control chaos and bifurcations, the state feedback method is implemented. Numerical simulations are also provided for the theoretical discussion. [ABSTRACT FROM AUTHOR]

In this paper, we have derived a discrete evolutionary Beverton–Holt population model. The model is built using evolutionary game theory methodology and takes into consideration the strong Allee effect related to predation saturation. We have discussed the existence of the positive fixed point and examined its asymptotic stability. Analytically, we demonstrated that the derived model exhibits Neimark–Sacker bifurcation when the maximal predator intensity is at lower values. All chaotic behaviors are justified numerically. Finally, to avoid these chaotic features and achieve asymptotic stability, we implement two chaos control methods. [ABSTRACT FROM AUTHOR]

This paper deals with the modeling of the immune system response to cancer cells. A mathematical model is proposed for a large system of interacting cells, by means of the mathematical methods of the kinetic theory for active particles. The first part of the paper deals with the assessment of the mathematical framework suitable for the derivation of specific models. Then a qualitative analysis is carried out to prove the existence of the solutions of the Cauchy problem related to the model. Some simulations visualize the applicability of the model to the description of biological events characterizing the immune competition. [ABSTRACT FROM AUTHOR]