Sequences of Gluing Bifurcations in an Analog Electronic Circuit

TL;DR

This paper experimentally investigates gluing bifurcations in an analog electronic circuit modeling a modified Lorenz system, revealing how parameter variations lead from periodic oscillations to chaos through a sequence of homoclinic bifurcations.

Contribution

It provides the first experimental observation of gluing bifurcations in an electronic circuit modeling a third-order dynamical system with quadratic nonlinearity.

Findings

Gluing bifurcations cause the merging of stable periodic orbits.

Parameter variation induces transition from periodic to chaotic dynamics.

Sequence of homoclinic bifurcations leads to chaos.

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.