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Path formulation for multiparameter D3-equivariant bifurcation problems
(2010-11-22)
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 ...
Path formulation for multiparameter D3-equivariant bifurcation problems
(2010-11-22)
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 ...
Bifurcations and multistability in the extended Hindmarsh-Rose neuronal oscillator
(2016-04-01)
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 ...
Some remarks on bifurcation analysis of a nonlinear vibrating system excited by a shape memory alloy material (SMA)
(2011-10-01)
In this paper, the dynamical response of a coupled oscillator is investigated, taking in consideration the nonlinear behavior of a SMA spring coupling the two oscillators. Due to the nonlinear coupling terms, the system ...
Some remarks on bifurcation analysis of a nonlinear vibrating system excited by a shape memory alloy material (SMA)
(2011-10-01)
In this paper, the dynamical response of a coupled oscillator is investigated, taking in consideration the nonlinear behavior of a SMA spring coupling the two oscillators. Due to the nonlinear coupling terms, the system ...
Transcritical and zero-Hopf bifurcations in the Genesio system
(2017-04-01)
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 ...
Degenerate hope bifurcations in Chua's system
(2009-02-01)
In this paper we study the local codimension one, two and three Hopf bifurcations which occur in the classical Chua's differential equations with cubic nonlinearity. A detailed analytical description of the regions in the ...
Degenerate hope bifurcations in Chua's system
(2009-02-01)
In this paper we study the local codimension one, two and three Hopf bifurcations which occur in the classical Chua's differential equations with cubic nonlinearity. A detailed analytical description of the regions in the ...
The Hopf bifurcation in the Shimizu-Morioka system
(Springer, 2015-02-01)
We study the local Hopf bifurcations of codimension one and two, which occur in the Shimizu-Morioka system. This system is a simplified model proposed for studying the dynamics of the well-known Lorenz system for large ...