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Transiently chaotic flows; ellipsoid equilibria; hidden attractors

In this article, a simple autonomous transiently chaotic flow with cubic nonlinearities is proposed. This system represents some unusual features such as having a surface of equilibria. We shall describe some dynamical properties and behaviours of this system in terms of eigenvalue structures, bifurcation diagrams, time series, and phase portraits. Various behaviours of this system such as periodic and transiently chaotic dynamics can be shown by setting special parameters in proper values. Our system belongs to a newly introduced category of transiently chaotic systems: systems with hidden attractors. Transiently chaotic behaviour of our proposed system has beenimplemented and tested by the OrCAD-PSpise software. We have found a proper qualitative similarity between circuit and simulation results.

SHIRIN PANAHI¹ ZAINAB ARAM¹ SAJAD JAFARI¹ VIET-THANH PHAM² CHRISTOS VOLOS³ KARTHIKEYAN RAJAGOPAL^{4 5}

1. Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413, Iran
2. School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Vietnam
3. Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloníki, Greece
4. Center for Nonlinear Dynamics, Department of Electrical and Communication Engineering, The PNG University of Technology, Lae, Papua New Guinea
5. Centre for Non-Linear Dynamics, Defense University, Bishoftu, Ethiopia

Published

1 March 2018

Manuscript received

10 July 2017

Manuscript revised

28 December 2017

Accepted

10 October 2017

Early published

Unedited version published online

Final version published online

8 February 2018