Hyperchaotic Self-Oscillations of Two-Stage Class C Amplifier With Generalized Transistors

2022

Mathematics

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This paper describes recent findings achieved during a numerical investigation of the circuit known as the Clapp oscillator. By considering the generalized bipolar transistor as an active element and after applying the search-for-chaos optimization approach, parameter regions that lead to either chaotic or hyperchaotic dynamics were discovered. For starters, the two-port that represents the transistor was firstly assumed to have a polynomial-forward trans-conductance; then the shape of trans-conductance changes into the piecewise-linear characteristics. Both cases cause vector field symmetry and allow the coexistence of several different attractors. Chaotic and hyperchaotic behavior were deeply analyzed by using standard numerical tools such as Lyapunov exponents, basins of attraction, bifurcation diagrams, and solution sensitivity. The structural stability of strange attractors observed numerically was finally proved via a real practical experiment: a flow-equivalent chaotic oscillator was constructed as the lumped electronic circuit, and desired attractors were captured and provided as oscilloscope screenshots.

Section: Mathematical Modelsmentioning

confidence: 99%

Chaotic and Hyperchaotic Dynamics of a Clapp Oscillator

2022

Mathematics

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“…More details including flow-equivalent circuit realization and experimental verification can be found in paper [115]. A hyperchaotic two-stage amplifier with the resonant load is addressed in work [116]. Each stage contains a generalized transistor, i.e., a two-port modeled by admittance parameters with nonlinear forward trans-conductance.…”

Section: Fourth-order Chaotic Oscillator One Step Toward Hyperchaosmentioning

confidence: 99%

Chaos in Analog Electronic Circuits: Comprehensive Review, Solved Problems, Open Topics and Small Example

2022

Mathematics

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This paper strives to achieve a comprehensive review of chaos in analog circuits and lumped electronic networks. Readers will be guided from the beginning of the investigations of simple electronic circuits to the current trends in the research into chaos. The author tries to provide the key references related to this issue, including papers describing modern numerical algorithms capable of localizing chaotic and hyperchaotic motion in complex mathematical models, interesting full on-chip implementations of chaotic systems, possible practical applications of entropic signals, fractional-order chaotic systems and chaotic oscillators with mem-elements.

“…Recent papers [15][16][17] admits non-ideal circuit model of bipolar transistor working as two-port described by following admittance parameters: linear input admittance, linear backward trans-conductance and nonlinear (with a saturation-type shape) forward trans-conductance of the form…”

Section: Mathematical Models Of Simplified Single Transistor Based Os...mentioning

confidence: 99%

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

2022

IEEE Access

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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.