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: the state of being divided into two branches or parts : the act of bifurcating.
What is the bifurcation control theory?
Bifurcation control refers to the task of designing a controller that can modify the bifurcation properties of a given nonlinear system, so as to achieve some desirable dynamical behaviors.
What are the conditions for bifurcation?
The bifurcation condition is ( tr A 0 = 0 , det A 0 0 ) (see Eq. (7.45)). At a Hopf bifurcation point, the eigenvalues of the stability matrix A 0 are purely imaginary, i.e., they are of the form i H , where H = ( det A 0 ) 1 / 2 .
What is the normal form of the bifurcation?
The normal form for a saddle-node bifurcation is given by . x=r+x2. The fixed points are x=r. Clearly, two real fixed points exist when r0.
What are the 4 types of bifurcation?
We now consider four classic bifurcations of one-dimensional nonlinear differential equations: saddle-node bifurcation, transcritical bifurcation, supercritical pitchfork bifurcation, and subcritical pitchfork bifurcation.
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Bifurcation diagrams are an effective way of representing the nature of the solutions of a one-parameter family of differential equations. Bifurcations for a one-parameter family of differential equations dx/dt=f(x) d x / d t = f ( x ) are rare. Bifurcations occur when f0(x0)=0 f 0 ( x 0 ) = 0 and f0(x0)=0.
What is the mathematical bifurcation theory?
Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations.
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by ML Saggio 2024 Cited by 5 Transitions between interictal and ictal states are modeled as bifurcations, enabling the definition of seizure classes in terms of onset/offset bifurcations.
normal form for the fold bifurcation is dx dt= a x2. (1). Theorem: If the function f(y, a) is smooth and. 1. f(0, 0) = 0. 2. fy(0, 0) = 0. 3. fyy(0, 0) 6= 0
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