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Unbounded dynamics in dissipative flows: Rössler model
2. Y.-C. Lai and T. Tél, “ Complex dynamics on finite-time scales,” Transient Chaos, Applied Mathematical Sciences Vol. 173 (Springer, New York, 2011), pp. xiv+497.
4. T. Tél and M. Gruiz, Chaotic Dynamics: An Introduction Based on Classical Mechanics (Cambridge University Press, 2006).
10. P. Collet and J.-P. Eckmann, Iterated Maps on the Interval as Dynamical Systems, Progress in Physics Vol. 1 (Birkhäuser, Boston, Mass., 1980).
14. R. Barrio, F. Blesa, S. Serrano, and A. Shilnikov, “ Global organization of spiral structures in biparameter space of dissipative systems with Shilnikov saddle-foci,” Phys. Rev. E 84, 035201 (2011).
18. E. J. Doedel, R. C. Paffenroth, A. R. Champneys, T. F. Fairgrieve, Y. A. Kuznetsov, B. E. Oldeman, B. Sandstede, and X. J. Wang, Auto2000: Continuation and Bifurcation Software for Ordinary Differential Equations (2000).
21. V. Castro, M. Monti, W. B. Pardo, J. A. Walkenstein, and E. Rosa, Jr., “ Characterization of the Rössler system in parameter space,” Int. J. Bifurcation Chaos 17, 965–973 (2007).
22. Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, Applied Mathematical Sciences Vol. 112, 3rd ed. (Springer-Verlag, New York, 2004).
23. J.-M. Ginoux, B. Rossetto, and L. O. Chua, “ Slow invariant manifolds as curvature of the flow of dynamical systems,” Int. J. Bifurcation Chaos 18, 3409–3430 (2008).
28. F. Verhulst, Methods and Applications of Singular Perturbations, Texts in Applied Mathematics Vol. 50 (Springer, New York, 2005).
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Transient chaos and unbounded dynamics are two outstanding phenomena that dominate in chaotic systems with large regions of positive and negative divergences. Here, we investigate the mechanism that leads the unbounded dynamics to be the dominant behavior in a dissipative flow. We describe in detail the particular case of boundary crisis related to the generation of unbounded dynamics. The mechanism of the creation of this crisis in flows is related to the existence of an unstable focus-node (or a saddle-focus) equilibrium point and the crossing of a chaotic invariant set of the system with the weak-(un)stable manifold of the equilibrium point. This behavior is illustrated in the well-known Rössler model. The numerical analysis of the system combines different techniques as chaos indicators, the numerical computation of the bounded regions, and bifurcation analysis. For large values of the parameters, the system is studied by means of Fenichel's theory, providing formulas for computing the slow manifold which influences the evolution of the first stages of the orbit.
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