In this paper we prove the global bifurcation theorem for the nonlinear Picard problem. The right-hand side function φ is a Caratheodory map, not differentiable at zero, but behaving in the neighbourhood of zero as specified in details below. We prove that in some interval [a, b] ⊂ R the Leray-Schauder degree changes, hence there exists the global bifurcation branch. Later, by means of some app...

<p style='text-indent:20px;'>In this paper we investigate a discrete-time predator-prey system with not only some constant parameters but also unfixed functional responses including growth rate function of prey, conversion factor and predation probability function. We prove that the maximal number fixed points is <inline-formula><tex-math id="M1">\begin{document}$ 3 $\end{docu...

In recent studies of the master mode-locking equation, a model for solid-state cavity laser that includes nonlocal terms, bifurcations from stationary to seemingly time-periodic solitary waves have been observed. To decide whether the mechanism is a Hopf bifurcation or a bifurcation from the essential spectrum, a general framework for the Evans function for equations with nonlocal terms is deve...

In this paper we study bifurcations in predator-prey systems with seasonal prey harvesting. First, when the seasonal harvesting reduces to constant yield, it is shown that various kinds of bifurcations, including saddle-node bifurcation, degenerate Hopf bifurcation, and Bogdanov– Takens bifurcation (i.e., cusp bifurcation of codimension 2), occur in the model as parameters vary. The existence o...

An adaptive oligopoly model, where the demand function is isoelastic and the competitors operate under constant marginal costs, is considered. The Cournot equilibrium point then loses stability through a subcritical Neimark bifurcation. The present paper focuses some global bifurcations, which precede the Neimark bifurcation, and produce other attractors which coexist with the still attractive ...

This study aims to classify the critical points of functions with 4 variables and 8 parameters, we found caustic for certain function spreading points. Finally, as an application, bifurcation solutions equation sixth order boundary conditions using Lyapunov-Schmidt method in variational case.