A simple anti-parallel diodes based chaotic jerk circuit with arcsinh function: theoretical analysis and experimental verification

Abstract

This paper introduces a novel autonomous chaotic jerk circuit with an antiparallel diodes pair whose mathematical model involves an inverse hyperbolic sine function in the form: $$f\left( x \right) = k - 2x + 4\arcsin h\left( {mx} \right)$$ where $$k$$ (i.e. a constant excitation source) controls the symmetry of the model while $$m$$ represents the slope of the inverse hyperbolic sine. The presence of the inverse hyperbolic sine is unusual provided that such types of circuits are connected to hyperbolic sine nonlinearity. The analysis of the model indicates that in case of a perfect symmetry ( $$k = 0.0$$ ), the system undergoes spontaneous symmetry breaking, period doubling scenario to chaos, symmetry recovering crisis, coexistence of multiple pairs of symmetric attractors, and coexisting symmetric bubbles of bifurcation. More complex and incoherent nonlinear dynamic patterns occur in the presence of symmetry perturbation ( $$k\ne 0.0$$ ) including for instance non-symmetric Hopf bifurcations, coexisting point attractor and limit cycle, coexisting asymmetric bubbles of bifurcations, critical transitions, and coexisting (i.e. up to five) non-symmetric periodic and chaotic attractors. The space magnetization resulting from the presence of various coexisting attractors is examined and illustrated by using basins of attraction. The predictions of theoretical investigations are supported by laboratory experimental tests based on a prototypal electronic circuit mounted on a breadboard.