Canonical Hyperchaotic Oscillators With Single Generalized Transistor and Generative Two-Terminal Elements

Abstract

This paper describes systematic design process toward third-order autonomous deterministic hyperchaotic oscillators with two coupled generative two-terminal elements. These active devices represent alternative to conventional dissipative accumulation elements such as capacitors and inductors. Analyzed network structures contain generalized bipolar transistor as only active element. Three different networks are studied, depending on common-electrode configurations. In each case, transistor is modelled using twoport admittance parameters with the non-zero linear backward and polynomial forward trans-conductance. As proved in paper, scalar nonlinearity caused by amplification property of transistor can push circuit into chaotic and, more interestingly, hyperchaotic steady states. Existence of parameter spaces leading to robust chaotic and hyperchaotic solution is documented by using concept of one-dimensional Lyapunov exponents and colored high-resolution surface-contour plots of two largest numbers. Geometrical structural stability of generated strange attractors is proved via construction of the flow-equivalent chaotic oscillator and real measurement. Plane projections of interesting observed attractors are captured by oscilloscope.INDEX TERMS Admittance parameters, bipolar transistor, frequency dependent negative resistor, chaos, chaotic oscillator, hyperchaos, Lyapunov exponents, strange attractors.

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