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Generating chaos via $$x|x|$$. (English) Zbl 1010.34033
Here, the authors discuss the existence of chaos for the following Duffing-like oscillator $\ddot x-ax +bx|x|=\varepsilon (-\zeta \dot x +c\sin (\omega t))$ by using the Melnikov-function method. It is shown that the piecewise quadraticfunction $$x|x|$$ can be seen as a chaos generator. Its physcial meaning as an energy function is explained.

##### MSC:
 34C28 Complex behavior and chaotic systems of ordinary differential equations 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
##### Keywords:
chaos; Duffing system; piecewise quadratic function
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