Bogdanov-Takens bifurcation with $ Z_2 $ symmetry and spatiotemporal dynamics in diffusive Rosenzweig-MacArthur model involving nonlocal prey competition

Improved Homoclinic Predictor for Bogdanov-Takens Bifurcation

An improved homoclinic predictor at a generic codim 2 Bogdanov-Takens (BT) bifucation is derived. We use the classical “blow-up” technique to reduce the canonical smooth normal form near a generic BT bifurcation to a perturbed Hamiltonian system. With a simple perturbation method, we derive explicit firstand second-order corrections of the unperturbed homoclinic orbit and parameter value. To ob...

a simple circuit model showing feature-rich Bogdanov-Takens bifurcation

A circuit model is proposed for studying the global behavior of the normal form describing the Bogdanov-Takens bifurcation, which is encountered in the study of autonomous dynamical systems arising in different branches of science and engineering. The circuit is easy-to-implement and one can experimentally study the rich dynamics and bifurcations simply by altering the values of some linear cir...

A Subshift of Finite Type in the Takens-Bogdanov Bifurcation with D 3 Symmetry

On the Takens-Bogdanov Bifurcation in the Chua’s Equation

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...

Takens–Bogdanov bifurcation of travelling-wave solutions in pipe flow

The appearance of travelling-wave-type solutions in pipe Poiseuille flow that are disconnected from the basic parabolic profile is numerically studied in detail. We focus on solutions in the twofold azimuthally-periodic subspace because of their special stability properties, but relate our findings to other solutions as well. Using timestepping, an adapted Krylov–Newton method and Arnoldi itera...