bifurcation theory

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bifurcation theory

[‚bī·fər′kā·shən ‚thē·ə·rē]
(mathematics)
The study of the local behavior of solutions of a nonlinear equation in the neighborhood of a known solution of the equation; in particular, the study of solutions which appear as a parameter in the equation is varied and which at first approximate the known solution, thus seeming to branch off from it. Also known as branching theory.
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Of course, he wouldn't, because of the bifurcation theory of Jekyll and Hyde.
It describes linear systems, existence and uniqueness, dynamical systems, invariant manifolds, the phase plane, chaotic dynamics, bifurcation theory, and Hamiltonian dynamics.
Kuznetsov, Elements of Applied Bifurcation Theory, Springer, New York, NY, USA, 3rd edition, 2004.
Bifurcation theory for finitely smooth planar autonomous differential systems was considered in .
In this paper we intend to research on this dynamic behavior in a discrete population model by using the bifurcation theory and normal form method; it is a fresh attempt different from previous related works.
According to the bifurcation theory , , the equation (1.1) possesses nontrivial solutions, which can be bifurcated from the bifurcation points.
Based on the bifurcation theory, we obtain new conditions of bifurcation with noise.
employed the Routh-Hurwitz stability criterion and bifurcation theory method to get a system equilibrium approximation near the zero value for the forward speed and front wheel steering angle, which revealed the vehicle's instability under high speeds and substantial steering [6, 7].
The remaining part of this section employs the four dimensional Hopf bifurcation theory and uses symbolic com putations to carry out the analysis of parametric variations concerning dynamical bifurcations.
Since the nonlinear bifurcation theory is utilized in solving nonlinear vehicle problems [1-3], the study on the calculation of critical speed gets a great deal of achievements [4, 5].
Kuznetsov, Elements of Applied Bifurcation Theory, Springer, Berlin, Germany, 2nd edition, 1997.
But in 1900, when Hilbert proposed his problems, there was no "bifurcation theory" yet.

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