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Bifurcation of periodic solutions to variational inequalities in ℝ κ based on Alexander-Yorke theorem

Milan Kučera (1999)

Czechoslovak Mathematical Journal

Variational inequalities U ( t ) ∈ K , ( U ˙ ( t ) - B λ U ( t ) - G ( λ , U ( t ) ) , Z - U ( t ) ) ≥ 0 for all Z ∈ K , a.a. t ∈ [ 0 , T ) are studied, where K is a closed convex cone in ℝ κ , κ ≥ 3 , B λ is a κ × κ matrix, G is a small perturbation, λ a real parameter. The assumptions guaranteeing a Hopf bifurcation at some λ 0 for the corresponding equation are considered and it is proved that then, in some situations, also a bifurcation of periodic solutions to our inequality occurs at some λ I ≠ λ 0 . Bifurcating solutions are obtained by the limiting process along branches of solutions to penalty problems starting at λ 0 constructed...

Bifurcations of the periodic solutions in symmetric systems

Alois Klíč (1986)

Aplikace matematiky

Bifurcation phenomena in systems of ordinary differential equations which are invariant with respect to involutive diffeomorphisms, are studied. Teh "symmetry-breaking" bifurcation is investigated in detail.

Bounded solutions on the Real line to non-autonomous Riccati Equations

Giuseppe Da Prato, Akira Ichikawa (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si dà un risultato di esistenza e unicità di una soluzione limitata in ] - ∞ , + ∞ [ per un'equazione di Riccati infinito-dimensionale.

Chaos in some planar nonautonomous polynomial differential equation

Klaudiusz Wójcik (2000)

Annales Polonici Mathematici

We show that under some assumptions on the function f the system ż = z ̅ ( f ( z ) e i ϕ t + e i 2 ϕ t ) generates chaotic dynamics for sufficiently small parameter ϕ. We use the topological method based on the Lefschetz fixed point theorem and the Ważewski retract theorem.

Chemotaxis models with a threshold cell density

Dariusz Wrzosek (2008)

Banach Center Publications

We consider a quasilinear parabolic system which has the structure of Patlak-Keller-Segel model of chemotaxis and contains a class of models with degenerate diffusion. A cell population is described in terms of volume fraction or density. In the latter case, it is assumed that there is a threshold value which the density of cells cannot exceed. Existence and uniqueness of solutions to the corresponding initial-boundary value problem and existence of space inhomogeneous stationary solutions are discussed....

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