Questions tagged [bifurcation]
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11 questions
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Is there an equivalent to the logistic map for a nonlinear path through some of the other nodules of the Mandelbrot set?
The logistic map can be related to the real axis of the Mandelbrot set, looking at the different cycle lengths as you pass through all the various nodules along the real axis. But there are other ...
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207
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Inverse problems and chaos theory
In the classical theory of inverse problems we want to recover an unknown $u \in U$ from its noisy measurements $y \in L^2$, where $U$ is a Banach space. In particular, we study the following problem:
...
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control of bifurcation in dynamical system by using normal form and feedback
enter image description here
enter image description here
the book "Approved for public release; distribution is unlimited.
THE CONTROL OF BIFURCATIONS
WITH ENGINEERING APPLICATIONS
by
Osa E. ...
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Identifying Saddle-node bifurcation of a 3D system of ODEs
I am trying to understand and prove the results shown in the following article. However, I am stuck at a point where it is stated that saddle-node bifurcation of periodic orbits occurs at ...
- 53
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Proving Hopf bifurcations for 3D system
I am working with a 3D continuous system of ODEs. I have found Hopf bifurcation numerically for a certain value of parameter. However, I want prove it analytically. Is it enough to show that the ...
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How to distinguish birth and death bifurcations?
Let $f : \mathbb{R} \to \mathbb{R}$ have a degenerate critical point at $x = 0 \, ($ie, $f(0) = f'(0) = f''(0) = 0)$.
Perturbing $f$ locally around $0$ may cause multiple scenarios:
Birth: the ...
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2
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1
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Proving period doubling bifurcation
I am working with a 3D continuous dynamical system. I have plotted the bifurcation diagram and found that period-doubling bifurcation occurs at a certain parameter value. However, I also want to prove ...
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Identifying bifurcation
[![enter image description here]] 1]1I am trying to analyze the bifurcation of a 3D continuous model. For a certain range of parameter values, the origin is always an unstable point, whereas the ...
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Periodic Orbit without Complex Eigenvalues
I am studying the following ODE system, representing a simple excitable circuit:
$$
\dot{V}_m = I_{app} - (V_m - \alpha_f PL(V_m) + \alpha_s PL(V_s))
$$
$$
\tau_s \dot{V}_s = V_m - V_s
$$
where
$$
PL(...
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bifurcation diagram of SI model in geogebra [closed]
I want to plot $I$ against $R_0$ in Geogebra (bifurcation diagram), these are related by the following system
$\begin{cases}S^\prime(t,S,I)=\frac{A}{b}-\frac{R_0SI}{S+I}-S\\I^\prime(t,S,I)=\frac{R_0SI}...
- 111
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Reason behind the names of sub and supercritical bifurcations
What is the reasoning behind the names sub- and super-critical bifurcations that occur in the context of pitchfork and Hopf bifurcations? Textbooks seem to introduce this terminology without any ...
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