Chaotic transitions Melnikov integral

In this section, we will introduce the Melnikov integral, which estimates the gaps between stable and unstable manifolds. Thus, if the Melnikov integral attains the value zero, this signals the existence of intersections between stable and unstable manifolds. If the intersection is transversal, it implies the existence of horseshoe dynamics [32], that is, chaotic behavior. On the other hand, if the intersection is tangent [11], it implies that the system is at a transition between different kinds of dynamics [12]. Such transitions of chaotic behavior are called crisis [13]. The tangency will be further analyzed in Section VII. 

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See also in sourсe #XX -- [ , , ]

See also in sourсe #XX -- [ , , ]

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