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.

Department of Radio Electronics Brno University of Technology Purkynova 118 612 00 Brno Czech Republic

Department of Theoretical Electrotechnics and Electrical Measurement Technical University of Kosice Letna 9 042 00 Kosice Slovakia

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