A Comparison Of Five Methods For Studying A Hyperchaotic Circuit

A hyperchaotic oscillator based on an LC oscillator and the Deliyannis single amplifier biquad (SAB), coupled by means of a diode, is studied. The inductor of the resonant circuit is realized in practice by using a generalized impedance converter (GIC). Various methods for detecting chaos, such as the Lyapunov exponents, the Lyapunov dimension, the Poincare map, the spectrum and the phase portraits, are used, in order to confirm the chaotic behaviour of the chaotic circuit. Experimental results fully coincide with theoretical and simulation results. The paper also attempts to answer the question 'which of the above methods is the most preferable, and why?'. It is concluded that the Lyapunov exponents, Lyapunov dimension and Poincare map constitute the more reliable methods of confirming chaos.