Bifurcation in a model of the population dynamics.
Bifurcation of an invariant torus of a system of differential equations in the degenerate case.
Bifurcation of multi-bump homoclinics in systems with normal and slow variables.
Bifurcation of periodic and chaotic solutions in discontinuous systems
Chaos generated by the existence of Smale horseshoe is the well-known phenomenon in the theory of dynamical systems. The Poincaré-Andronov-Melnikov periodic and subharmonic bifurcations are also classical results in this theory. The purpose of this note is to extend those results to ordinary differential equations with multivalued perturbations. We present several examples based on our recent achievements in this direction. Singularly perturbed problems are studied as well. Applications are given...
Bifurcation of periodic points and normal form theory in reversible diffeomorphisms
Bifurcation of periodic solutions from inversion of stability of periodic O.D.E.'S.
Bifurcation of periodic solutions in differential inclusions
Ordinary differential inclusions depending on small parameters are considered such that the unperturbed inclusions are ordinary differential equations possessing manifolds of periodic solutions. Sufficient conditions are determined for the persistence of some of these periodic solutions after multivalued perturbations. Applications are given to dry friction problems.
Bifurcation of periodic solutions to differential inequalities in
Bifurcation of periodic solutions to variational inequalities in based on Alexander-Yorke theorem
Variational inequalities are studied, where is a closed convex cone in , , is a matrix, is a small perturbation, a real parameter. The assumptions guaranteeing a Hopf bifurcation at some 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 . Bifurcating solutions are obtained by the limiting process along branches of solutions to penalty problems starting at constructed...
Bifurcation of solutions of nonlinear Sturm-Liouville problems.
Bifurcation of solutions of separable parameterized equations into lines.
Bifurcations and chaos in a periodically forced prototype adaptive control system
Bifurcations de polycycles infinis pour les champs de vecteurs polynomiaux du plan
Bifurcations of limit cycles from cubic Hamiltonian systems with a center and a homoclinic saddle-loop.
It is proved in this paper that the maximum number of limit cycles of system⎧ dx/dt = y⎨⎩ dy/dt = kx - (k + 1)x2 + x3 + ε(α + βx + γx2)yis equal to two in the finite plane, where k > (11 + √33) / 4 , 0 < |ε| << 1, |α| + |β| + |γ| ≠ 0. This is partial answer to the seventh question in [2], posed by Arnold.
Branching of periodic orbits from Kukles isochrones.
Branching of periodic orbits in Hamiltonian and reversible systems
Centres and limit cycles for an extended Kukles system.
Champs lents-rapides complexes à une dimension lente
Chaotic behavior and modified function projective synchronization of a simple system with one stable equilibrium
By introducing a feedback control to a proposed Sprott E system, an extremely complex chaotic attractor with only one stable equilibrium is derived. The system evolves into periodic and chaotic behaviors by detailed numerical as well as theoretical analysis. Analysis results show that chaos also can be generated via a period-doubling bifurcation when the system has one and only one stable equilibrium. Based on Lyapunov stability theory, the adaptive control law and the parameter update law are derived...
Complete polynomial vector fields in simplexes with application to evolutionary dynamics.