We have found new dissipative solitons of the complex cubic-quintic Ginzburg-Landau equation with extreme amplitudes and short duration. At certain range of the equation parameters, these extreme spikes appear in pairs of slightly unequal amplitude. The bifurcation diagram of pulse amplitude versus dispersion parameter is constructed. c © 2015 Optical Society of America OCIS codes: 060.5530, 14...

In this paper, we investigate the problem of bifurcation control for a delayed logistic growth model. By choosing the timedelay as the bifurcation parameter, we present a Proportional - Derivative (PD) Controller to control Hopf bifurcation. We show that the onset of Hopf bifurcation can be delayed or advanced via a PD Controller by setting proper controlling parameter. Under consideration mode...

An epidemic model with standard incidence rate and saturated treatment function of infectious individuals is proposed to understand the effect of the capacity for treatment of infective individuals on the disease spread. The treatment function in this paper is a continuous and differential function which exhibits the effect of delayed treatment when the rate of treatment is lower and the number...

In this paper we deal with Robin and Neumann parametric elliptic equations driven by a nonhomogeneous differential operator and with a reaction that exhibits competing nonlinearities (concave-convex nonlinearities). For the Robin problem and without employing the Ambrosetti-Rabinowitz condition, we prove a bifurcation theorem for the positive solutions for small values of the parameter λ > 0. F...

An algorithm to detect homoclinic twist bifurcation points in Z2 symmetric autonomous systems of ordinary differential equations in R4 along curves of symmetric homoclinic orbits to hyperbolic equilibria has been developed.We show convergence of numerical approximations to homoclinic twist bifurcation points in such systems. A test function is defined on the homoclinic solutions, which has a re...

We prove that the study of Rimmer bifurcation of symmetric fixed points in two–dimensional discrete reversible dynamical systems can be achieved analysing either bifurcation of critical points of a symmetric Hamiltonian function or the bifurcation of symmetric equilibrium points for a nonconservative reversible vector field. We give the normal forms for generating functions of area preserving r...

One of the major routes to chaotic scattering is through an abrupt bifurcation by which a nonattracting chaotic saddle is created as a system parameter changes through a critical value. In a previously investigated case, however, the fractal dimension of the set of singularities in the scattering function changes continuously through the bifurcation. We describe a type of abrupt bifurcation to ...