Now showing items 1-10 of 281
Path formulation for multiparameter D3-equivariant bifurcation problems
We implement a singularity theory approach, the path formulation, to classify D3-equivariant bifurcation problems of corank 2, with one or two distinguished parameters, and their perturbations. The bifurcation diagrams are ...
Existence of secondary bifurcations or isolas for PDEs
(PERGAMON-ELSEVIER SCIENCE LTD, 2011)
In this paper, we introduce a method to conclude about the existence of secondary bifurcations or isolas of steady state solutions for parameter dependent nonlinear partial differential equations. The technique combines ...
Transcritical and zero-Hopf bifurcations in the Genesio system
In this paper we study the existence of transcritical and zero-Hopf bifurcations of the third-order ordinary differential equation x⃛ + ax¨ + bx˙ + cx- x2= 0 , called the Genesio equation, which has a unique quadratic ...
Bifurcations and multistability in the extended Hindmarsh-Rose neuronal oscillator
We report on the bifurcation analysis of an extended Hindmarsh-Rose (eHR) neuronal oscillator. We prove that Hopf bifurcation occurs in this system, when an appropriate chosen bifurcation parameter varies and reaches its ...
Um estudo de bifurcações de codimensão dois de campos de vetores
(Universidade Estadual Paulista (UNESP), 2014)
SHILNIKOV BIFURCATION: STATIONARY QUASI-REVERSAL BIFURCATION
(WORLD SCIENTIFIC PUBL CO PTE LTD, 2008-07)
A generic stationary instability that arises in quasi-reversible systems is studied. It is characterized by the confluence of three eigenvalues at the origin of complex plane with only one eigenfunction. We characterize ...
Zero-Hopf bifurcation in a Chua system
A zero-Hopf equilibrium is an isolated equilibrium point whose eigenvalues are ±ωi≠0 and 0. In general for a such equilibrium there is no theory for knowing when it bifurcates some small-amplitude limit cycles moving the ...
NONDEGENERATE UMBILICS, THE PATH FORMULATION and GRADIENT BIFURCATION PROBLEMS
(World Scientific Publ Co Pte Ltd, 2009-09-01)
Parametrized contact-equivalence is a successful theory for the understanding and classification of the qualitative local behavior of bifurcation diagrams and their perturbations. Path formulation is an alternative point ...
3-Dimensional hopf bifurcation via averaging theory
We consider the Lorenz system ẋ = σ(y - x), ẏ = rx - y - xz and ż = -bz + xy; and the Rössler system ẋ = -(y + z), ẏ = x + ay and ż = b - cz + xz. Here, we study the Hopf bifurcation which takes place at q± = (±√br - b,±√br ...