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Numerical semi-global analysis of a 1:2 resonant Hopf-Hopf bifurcation
(Elsevier Science, 2013-03)
In this paper, a numerical semi-global analysis of the dynamics near a 1:2 resonant Hopf-Hopf bifurcation on a four-dimensional mathematical model of a simple nonlinear oscillator is performed. The 1:2 resonant Hopf-Hopf ...
Zero-Hopf bifurcation in a Chua system
(2017-10-01)
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 ...
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 ...
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 ...
A Degenerate 2:3 Resonant Hopf-Hopf Bifurcation as Organizing Centre of the Dynamics: Numerical Semi-Global Results
(Siam Publications, 2015-07)
In this paper a degenerate case of a 2:3 resonant Hopf–Hopf bifurcation is studied. This codimensionfour bifurcation occurs when the frequencies of both Hopf bifurcation branches have the relation 2/3, and one of them ...
Hopf and zero-Hopf bifurcations in the Hindmarsh–Rose system
(2016-02-01)
We prove the existence of the classical Hopf bifurcation and of the zero-Hopf bifurcation in the Hindmarsh–Rose system. For doing this, some adequate change in parameters must be done in order that the computations become easier.
Zero-Hopf bifurcation in the FitzHugh-Nagumo system
(2015-11-30)
We characterize the values of the parameters for which a zero-Hopf equilibrium point takes place at the singular points, namely, O (the origin), P+, and P- in the FitzHugh-Nagumo system. We find two two-parameter families ...
DEGENERATE HOPF BIFURCATIONS IN CHUA'S SYSTEM
(World Scientific Publ Co Pte Ltd, 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 ...
Evolution towards the steady state in a hopf bifurcation: A scaling investigation
(2018-01-01)
Some scaling properties describing the convergence for the steady state in a Hopf bifurcation are discussed. Two different procedures are considered in the investigation: (i) a phenomenological description obtained from ...
Stability and Hopf bifurcation in an hexagonal governor system
(PERGAMON-ELSEVIER SCIENCE LTD, 2008)
In this paper we study the Lyapunov stability and the Hopf bifurcation in a system coupling an hexagonal centrifugal governor with a steam engine. Here are given sufficient conditions for the stability of the equilibrium ...