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2014
In this chapter we study a bifurcation characterized by a zero eigenvalue and a pair of nonzero purely imaginary eigenvalues of the linearization transverse to a plane of equilibria. It turns out that instead we can study a one-parameter family of lines in a system depending on one parameter.
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In this chapter we study a bifurcation characterized by a zero eigenvalue and a pair of nonzero purely imaginary eigenvalues of the linearization transverse to a plane of equilibria. It turns out that instead we can study a one-parameter family of lines in a system depending on one parameter.
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2018
The Hopf bifurcation theorem provides an effective criterion for finding periodic solutions for ordinary differential equations. Although various proofs of this classical theorem are known, there seems to be no easy way to arrive at the goal.
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The Hopf bifurcation theorem provides an effective criterion for finding periodic solutions for ordinary differential equations. Although various proofs of this classical theorem are known, there seems to be no easy way to arrive at the goal.
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Nonlinear Analysis: Theory, Methods & Applications, 1989
It is the purpose of this paper to study the behaviour of linear dominated systems for large |x|. It is reasonable to assume that, in this region, the linear part will determine the local and (perhaps) global dynamics of the system. Under fairly weak conditions, as a parameter of the system is varied, a bifurcation occurs which generates arbitrarily ...
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It is the purpose of this paper to study the behaviour of linear dominated systems for large |x|. It is reasonable to assume that, in this region, the linear part will determine the local and (perhaps) global dynamics of the system. Under fairly weak conditions, as a parameter of the system is varied, a bifurcation occurs which generates arbitrarily ...
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Hopf bifurcation by frustrated drifts
Physical Review E, 1996Rainer Schmitz, Walter Zimmermann
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