One of the most important tasks in nonlinear dynamics is the determination of bifurcation sets of various dynamical systems. If the dynamical equations are known, bifurcation points in parameter space can be detected by solving some specific fixed point equations. Using suitable continuation algorithms these bifurcation points can be traced in parameter space in order to compute bifurcation cur...

In this paper, we have considered a system of delay differential equations. The system without delayed arises in the Lengyel–Epstein model. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. Linear stability is investigated and existence of Hopf bifurcation is demonstrated via analyzing the associated characteristic equation. For the Hopf bifurcation analysis, th...

In this paper, local bifurcation of a discrete two patch logistic metapopulation is discussed. By the central manifold method, flip bifurcation can be analyzed at the positive fixed point from the viewpoint of the dynamical system, and the system can not undergo a fold bifurcation. Simulations on this model show the discrete model can have rich dynamical behaviors. The state feedback control is...

We consider the delayed feedback control method for stabilization of unstable rotating waves near a fold bifurcation. Theoretical analysis of a generic model and numerical bifurcation analysis of the rate-equations model demonstrate that such orbits can always be stabilized by a proper choice of control parameters. Our paper confirms the recently discovered invalidity of the so-called "odd-numb...

Recently, there has been an interest in designing systems that employ buckling bifurcation as a desired mechanism to generate motion and/or form. As buckling has traditionally been considered a failure mode to be avoided, computational tools for predicting the state of the system after buckling are not well developed. For example, modules for post-bifurcation studies are not available in most o...

The main modes of behavior of a food chain model, composed of logistic prey and Holling type II predator and superpredator, are discussed in this paper. The study is carried out through bifurcation analysis, alternating between a normal form approach and numerical continuation. The two-parameter bifurcation diagram of the model contains Hopf, fold and transcritical bifurcation curves of equilib...

The analysis of the Takens-Bogdanov bifurcation of the equilibrium at the origin in the Chua’s equation with a cubic nonlinearity is carried out. The local analysis provides, in first approximation, different bifurcation sets, where the presence of several dynamical behaviours (including periodic, homoclinic and heteroclinic orbits) is predicted. The local results are used as a guide to apply t...