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First of all, there are no universally accepted defintions of Turing pattern, excitable or oscillatory medium. This is somewhat understandable as there is no real need for one. All these terms describe very huge classes of phenomena and thus you do not form any statements requiring a precise definitions such as: “If X is an oscillatory medium, then …” That ...


2

Consider a variant of the FitzHugh–Nagumo system: $$ \begin{align}\dot{x} &= x (a - x) (x - 1) - y \\ \dot{y} &= bx - cy \end{align}$$ with parameters like $a=-0.02; b=0.01; c=0.02$. The eigenvalues of the Jacobian at $(0,0)$ (which is a fix point) are $±\frac{\sqrt{6}}{25}i$. The attractor for this system looks like this: Obviously, this is ...



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