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Coexistence of small and large amplitude limit cycles of polynomial differential systems of degree four

Eduardo Sáez, Eduardo Stange, Iván Szántó (2007)

Czechoslovak Mathematical Journal

A class of degree four differential systems that have an invariant conic $x^{2} + C y^{2} = 1$ , $C \in ℝ$ , is examined. We show the coexistence of small amplitude limit cycles, large amplitude limit cycles, and invariant algebraic curves under perturbations of the coefficients of the systems.

Complementary analysis of the initial value problem for a system of o.d.e. modelling the immune system after vaccinations

Urszula Foryś, Norbert Żołek (2000)

Applicationes Mathematicae

Complementary analysis of a model of the human immune system after a series of vaccinations, proposed in [7] and studied in [6], is presented. It is shown that all coordinates of every solution have at most two extremal values. The theoretical results are compared with experimental data.

Conflict-Controlled Processes Involving Fractional Differential Equations with Impulses

Matychyn, Ivan, Chikrii, Arkadii, Onyshchenko, Viktoriia (2012)

Mathematica Balkanica New Series

MSC 2010: 34A08, 34A37, 49N70Here we investigate a problem of approaching terminal (target) set by a system of impulse differential equations of fractional order in the sense of Caputo. The system is under control of two players pursuing opposite goals. The first player tries to bring the trajectory of the system to the terminal set in the shortest time, whereas the second player tries to maximally put off the instant when the trajectory hits the set, or even avoid this meeting at all. We derive...

Constructing soliton and kink solutions of PDE models in transport and biology.

Vladimirov, Vsevolod A., Kutafina, Ekaterina V., Pudelko, Anna (2006)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Contributions of Alan C. Lazer to mathematical population dynamics.

Cosner, Chris (2000)

Electronic Journal of Differential Equations (EJDE) [electronic only]