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The Scientific World Journal
Volume 2014, Article ID 239407, 12 pages
Research Article

Dynamical Tangles in Third-Order Oscillator with Single Jump Function

1Department of Radio Electronics, Brno University of Technology, Purkynova 118, 612 00 Brno, Czech Republic
2Department of Theoretical Electrotechnics and Electrical Measurement, Technical University of Kosice, Letna 9, 042 00 Kosice, Slovakia

Received 16 July 2014; Revised 18 September 2014; Accepted 18 September 2014; Published 3 December 2014

Academic Editor: Esteban Tlelo-Cuautle

Copyright © 2014 Jiří Petržela et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This contribution brings a deep and detailed study of the dynamical behavior associated with nonlinear oscillator described by a single third-order differential equation with scalar jump nonlinearity. The relative primitive geometry of the vector field allows making an exhaustive numerical analysis of its possible solutions, visualizations of the invariant manifolds, and basins of attraction as well as proving the existence of chaotic motion by using the concept of both Shilnikov theorems. The aim of this paper is also to complete, carry out and link the previous works on simple Newtonian dynamics, and answer the question how individual types of the phenomenon evolve with time via understandable notes.