Canonization of dynamical system representation using trivial linear transformations

This brief paper brings a demonstration how the linear transformation of the coordinates including state variable offsets can simplify the final circuit realization of a third-order autonomous deterministic dynamical system. The structures of the individual derived analog oscillators are canonical i...

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Bibliographic Details
Main Authors: Petrzela, J., Hrubos, Z., Gotthans, T.
Format: Conference Proceeding
Language:English
Subjects:
analog oscillator
Chaos
Circuit synthesis
Mathematical model
modern active elements
Oscillators
Resistors
RLC circuits
third-order system
Transfer functions
Vectors
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Summary:This brief paper brings a demonstration how the linear transformation of the coordinates including state variable offsets can simplify the final circuit realization of a third-order autonomous deterministic dynamical system. The structures of the individual derived analog oscillators are canonical in the sense of minimum active devices utilized to synthesize both linear and nonlinear part of the vector field. Since the studied mathematical models consist of two quadratic polynomials maximal network design efficiency provided by multiplier transfer function must be achieved. Several implementations have been verified by using Orcad Pspice circuit simulator.