Analytical study of the double-hook attractor

The author investigates a large class of three-region, piecewise-linear, continuous vector fields on R³, termed the double-hook family F_s, which is a derivative of the well-known double-scroll circuit family and exhibits chaotic behavior both numerically and experimentally. The author performs a comprehensive analysis of the family´s piecewise-linear geometry, discusses the double-hook attractor´s structure, and presents a normal form equation for the family´s dynamics. He then commences a detailed qualitative study of its behavior by means of characteristic Poincare maps, after which he applies the Sil´nikov´s method to establish formally the existence of horseshoe chaos for a particular member of F_s. The present results are extended to the complementary dual double-hook family