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‘Lorenz attractor’ from an electrical circuit with uncoupled continuous piecewise‐linear resistor
Author(s) -
Tokunaga R.,
Komuro M.,
Matsumoto T.,
Chua L. O.
Publication year - 1989
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490170108
Subject(s) - attractor , lorenz system , piecewise linear function , resistor , chaotic , piecewise , mathematics , nonlinear system , mathematical analysis , control theory (sociology) , topology (electrical circuits) , physics , computer science , voltage , quantum mechanics , combinatorics , control (management) , artificial intelligence
We present a simple piecewise‐linear circuit which exhibits a chaotic attractor similar to that observed from the well‐known Lorenz equation. Whereas the non‐linearities in the Lorenz equation consists of two product terms between two state variables, the non‐linearities in our circuit consists of two ‘ uncoupled ’ 2‐terminal continuous non‐linear resistors, each characterized by a 2‐segment v‐i characteristic. Both experiments and computer simulations of this circuit confirm a Lorenz‐like strange attractor. the nature of the trajectories associated with this attractor is analysed and explained with the help of the circuit's piecewise‐linear‐geometry.