Construction and analysis of symmetric Sprott B multi-attractors with electric implementation

Abstract

Abstract In chaos theory, a number of systems and models which apparently contain simple ordinary differential equations (ODEs) turn out to show a dynamic characterized by complicated behaviors and complex trajectories. One of such systems is the Sprott B model. We construct some set of multi-attractors based on the Sprott B model where additional parameters and operators are considered. After summarizing important preliminaries relevant to simple chaotic differential systems, the model is firstly solved analytically and numerically, then graphical simulations are provided. The later show coexistence and evolution of two chaotic attractors in a symmetrical representation. Lastly, similar results and expected outcomes are recovered via an electrical circuit implementation, realized using the Field Programmable Gate Array (FPGA) board, the Digital-to-Analog Converter (DAC) and the Rigol Oscilloscope. They also show progressing sets of coexisting multi-attractors.