An exact homoclinic orbit and its connection with the Rössler system. (English) Zbl 1396.37027
Summary: In this letter, we consider a three parameter unfolding of a linear degeneracy corresponding to a triple-zero eigenvalue of an equilibrium point. Using blow-up techniques, we obtain a system where an exact homoclinic connection is determined. The numerical continuation of this global connection shows that it exhibits three different kinds of codimension-two degeneracies. Finally, these same codimension-two homoclinic bifurcations are detected in the Rössler system, ensuring in this way the existence of chaotic dynamics.
MSC:
| 37C29 | Homoclinic and heteroclinic orbits for dynamical systems |
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