Bautin bifurcation
نویسندگان
چکیده
منابع مشابه
Nonlinear Coupling near a Degenerate Hopf (Bautin) Bifurcation
A nonlinearly coupled system of bistable (fixed point and limit cycle) differential equations is analyzed. The nonlinear equations arise from the first several terms in the normal form expansion near a Bautin bifurcation. Existence and stability of in-phase and out-of-phase periodic solutions to a pair of identical systems are explored. Existence, uniqueness, and stability of traveling wave sol...
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The existence of periodic solutions for evolution equations is of certain interest for both pure and applied mathematicians. Even for bidimensional systems of differential equations the detection of limit cycles by theoretical means is difficult. The bifurcation theory offers a strong tool for finding limit cycles, namely the theory concerning the Hopf bifurcation (when there is a varying param...
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In the field of economic growth, a huge interest has been devoted to explain the mechanisms through which a nonlinear system looses its stability and starts to oscillate around the steady state. Since the seminal Kalekian analysis, limit cycles represent the theoretical way of characterizing the emergence of persistent oscillations of macro-economic variables, namely the rise of indeterminacy p...
متن کاملBautin Ideals and Taylor Domination
We consider families of analytic functions with Taylor coefficients-polynomials in the parameter λ: fλ(z) = ∑∞ k=0 ak(λ)z k, ak ∈ C[λ]. Let R(λ) be the radius of convergence of fλ. The “Taylor domination” property for this family is the inequality of the following form: for certain fixed N and C and for each k ≥ N + 1 and λ, |ak(λ)|R(λ) ≤ C max i=0,...,N |ai(λ)|R(λ). Taylor domination property ...
متن کاملSubcritical Elliptic Bursting of Bautin Type
Bursting behavior in neurons is a recurrent transition between a quiescent state and repetitive spiking. When the transition to repetitive spiking occurs via a subcritical Andronov–Hopf bifurcation and the transition to the quiescent state occurs via double limit cycle bifurcation, the burster is said to be of subcritical elliptic type. When the fast subsystem is near a Bautin (generalized Hopf...
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ژورنال
عنوان ژورنال: Scholarpedia
سال: 2007
ISSN: 1941-6016
DOI: 10.4249/scholarpedia.1853