# Questions tagged [bifurcation]

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### Energy delivered to unstable limit cycle

For a given family of stable and unstable $T$-periodic limit cycles $\Gamma$ forming a manifold $\mathcal{M}\subset \mathbb{R}^n\times \mathbb{R}^p$ of some (nonconservative) $p$-parametric $n$-...
• 101
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### Phase space portrait for dynamical system with Bifurcations

I have this dynamical system $$x'=y, y'=-x^3-y+mx$$ and I want to draw the phace space diagram for $m=-1/8, m=1/4,$ the bifurcation points. 1st of all I cant find what kind of bifruction I have( I go ...
1 vote
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### Inhomogeneous Brusselator model

I am studying a Brusselator model which includes inhomogeneous terms such as $\nabla ^2 x$ and $\nabla^2 y$ in the following way \begin{aligned} &\partial_{\tau} x=a-(b+1) x+x^{2} y+d_{X} \nabla^{...
• 121
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### Graph Interpretation of Fold of Cyclic Bifurcation

I was studying about local bifurcations of cycles, and the basic type of it was the cyclic fold. According to the textbook, cyclic fold bifucation was the meaning of one of those that is, for two ...
• 101
1 vote
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### Terminology for scenario when energy of system $E(\theta_1,\ldots,\theta_k)$ with $k$ real parameters, is minimum whenever $\theta_1=c$ (fixed value)

Disclaimer. I'm not a physicist. Consider a physical system whose "energy" $E$ is a function of $k$ real parameters $\theta = (\theta_1,\ldots,\theta_k) \in \mathbb R^k$. Let $E_{\min}$ be ...
• 181
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