Experimental confirmation of the period-adding route to chaos in a nonlinear circuit

Abstract

Experimental confirmation has been made on a negativeresistance oscillator circuit which exhibits the new period-adding route to chaos recently reported by Kaneko on a discrete map. The nonlinear element in the circuit is a negative-resistance device synthesized by using two bipolar transistors and four positive linear resistors. This circuit exhibits a new route to chaos; namely, through period-adding where the periods of two successive periodic waveforms belonging to each periodadding sequence differ by one; i.e., from period <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n - 1</tex> or <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n + 1</tex> . The transition to chaos (after one or more periodic states) resulted directly from a loss of stability of a periodic state at a bifurcation point. Several general features of the periodic-chaotic transition sequence have been observed and presented.