A new 3D chaotic system with golden proportion equilibria: Analysis and electronic circuit realization

Authors:
İHsan Pehlivan;YıLmaz UyaroğLu
Affiliations:
Sakarya University, Faculty of Technology, Department of Electrical and Electronics Eng., Esentepe Campus, Serdivan 54187, Sakarya, Turkey;Sakarya University, Engineering Faculty, Electrical Electronics Eng. Department, Esentepe Campus, Serdivan 54187, Sakarya, Turkey
Venue:
Computers and Electrical Engineering
Year:
2012

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Abstract

This article introduces a new three-dimensional quadratic continuous autonomous chaotic system with golden proportion equilibria, which can generate single folded attractor. Some basic dynamical behaviors and the dynamical structure of the new chaotic system are investigated either analytically or numerically. Finally, the chaos generator of the new chaotic system was designed, simulated and experimentally confirmed via a novel electronic circuit design. A good qualitative agreement is illustrated between the simulations and the experimental results. It is convenient to use the new system to purposefully generate chaos in chaos applications. The new system has eight terms, two quadratic nonlinearities and two parameters (a and b). The new chaotic attractor equations have three equilibrium points and more interestingly the equilibrium points have golden proportion values.