A 2D Hyperchaotic Map: Amplitude Control, Coexisting Symmetrical Attractors and Circuit Implementation

An absolute value function was introduced for chaos construction, where hyperchaotic oscillation found with amplitude rescaling. The nonlinear term brings the convenience control. Two regimes of control including total and partial are discussed, attractor can be rescaled separately by two independent coefficients. Symmetrical pairs coexisting attractors captured corresponding initial conditions. Circuit implementation platform STM32 is consistent numerical exploration theoretical observation. This finding helpful promoting discrete map application, realized in an easy way symmetrical sequences opposite polarity obtained.