Sequences of Gluing Bifurcations in an Analog Electronic Circuit

Abstract

We report on the experimental investigation of gluing bifurcations in the analog electronic circuit which models a dynamical system of the third order: Lorenz equations with an additional quadratic nonlinearity. Variation of one of the resistances in the circuit changes the coefficient at this nonlinearity and enables transition from the Lorenz route to chaos to a different scenario which leads, through the sequence of homoclinic bifurcations, from periodic oscillations of the voltage to the chaotic state. A single bifurcation "glues" in the phase space two stable periodic orbits and creates a new one, with the doubled length: a bifurcation sequence results in the birth of the chaotic attractor.