Symmetry-breaking, amplitude control and constant Lyapunov exponent based on single parameter snap flows

In this paper, we introduce a novel snap system with a unique parameterized piecewise quadratic nonlinearity in the form $$\psi _{n} \left( x \right) =x-n\left| x \right| -\mathrm{d}x\left| x \right| $$ where n controls the symmetry of the system and serves as total amplitude control of the signals. The model is described by a continuous time 4D autonomous system (ODE) with smooth conditional nonlinearity. We study the chaos mechanism with respect to system parameters both in the symmetric and asymmetric modes of oscillations by exploiting bifurcation diagrams, basin of attractions and phase portraits as main tools. In particular, for $$n=0$$ , the system displays a perfect symmetry and develops rich dynamics including period doubling sequences, merging crisis, hysteresis, and coexisting multiple symmetric attractors. For $$n\ne 0$$ , the system is non-symmetric and the space magnetization induced more complex and striking effects including asymmetric double scroll strange attractors, parallel branches, and asymmetric basin boundary leads to many coexisting asymmetric stable states and so on. Apart from all these complex and rich phenomena, many others including offset-boosting with total amplitude control, and antimonotonicity are also presented. Finally, Pspice based simulations of the proposed system are included.