Absrrucf-This paper provides a rigorous mathematical proof that the double scroll is indeed chaotic. Our approach is to derive a linearly equitdent class of piecewise-linear differential equations which includes the double scroll as a special case. A necessary and sufficient condition for two such piecewise-linear vector fields to be linearly equivalent is that their respective eigenvalues be a...

Figure 1: Scroll wave turbulence developed from a scroll with a curved filament. Simulation of FitzHugh-Nagumo model in 3D, parameters as in (Biktashev 1998). Red surfaces are fronts (u=0,v<0) blue surfaces are backs (u=0,v>0) of excitation waves, and yellow lines are singularities (u=0,v=0)rotating around slowly moving scroll filaments, where u,v are respectively the activator and inhibitor fi...

A new approach for generating -scroll attractors is introduced. It is demonstrated that -scroll attractors can be generated using a simple sine or cosine function. A guideline is given so that a different number of scrolls can be designed easily by modifying two variables in the function. An electronic circuit is also designed for the implementation and the observation of a 9-scroll attractor i...

Controlling chaos has become a challenging topic in nonlinear dynamics. It has been studied in many scientific and engineering fields such as physics, chemistry, electrical circuit, etc., and several extension and applications of the original OGY control method [1] have been reported [2–6]. Chua’s circuit is known as an electrical circuit and having the ability of generating chaos [7]. Recent r...

We investigate the structure of a variety new Moishezon twistor spaces, by utilizing pluri-half-anti-canonical map from spaces. Each these spaces is bimeromorphic to double covering scroll planes over rational normal curve, and branch divisor cover cut quartic hypersurface. In particular, has pencil Del Pezzo surfaces degree two. Correspondingly, have with big anti-canonical class. The base loc...