Abstract. We present two dual oscillating circuits, each with five bifurcating parameters and one nonlinear element of cubic current-voltage characteristics. The circuits can be considered as two coupled oscillators (linear and nonlinear). Bifurcation diagrams of the circuits show a rather surprising result that the bifurcation patterns are of the Farey sequence structure and the circuits' dynamics is of a fractal type. The circuits' fractal dimensions of the box counting (capacity) algorithm, Kaplan-Yorke (Lyapunov) type and its modified (improved) version are all estimated to be between 2.26 and 2.52. The circuits show a wide spectrum of interesting dynamical properties. Our analysis is based on numerical calculations which confirm a close relationship of the circuits' bifurcation patterns with those of the Ford circles and Stern-Brocot trees.

Received: July 5, 2011

AMS Subject Classification: 47N70, 34C15, 37M20, 28A80

Key Words and Phrases: oscillating circuits, bifurcations, singularly perturbed systems, farey sequence, Stern-Brocot tree, Ford circles, fractals

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