Analytical study of the double-hook attractor

The author investigates a large class of three-region, piecewise-linear, continuous vector fields on R/sup 3/, termed the double-hook family F/sub 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/sub s/. The present results are extended to the complementary dual double-hook family.<>