Effects of symmetric and asymmetric nonlinearity on the dynamics of a novel chaotic jerk circuit: Coexisting multiple attractors, period doubling reversals, crisis, and offset boosting

Abstract

Abstract A novel self-driven RC chaotic jerk circuit with the singular feature of having a smoothly adjustable nonlinearity and symmetry is proposed and investigated. The novel chaotic circuit is mathematically modeled by a third order system with a single nonlinear term in the form ϕ k ( x ) = 0.5 ( exp ( k x ) − exp ( − x ) ) where parameter k maps a smoothly adjustable control resistor. Obviously for k = 1 , the system is point symmetric with respect to the origin of the system coordinates since the nonlinear term reduces to the hyperbolic sine function. The case k ≠ 1 corresponds to a non-symmetric system. The numerical experiment reveals a plethora of events including period doubling route to chaos, hysteresis, periodic windows, asymmetric double scroll chaos, symmetric double scroll chaos, and coexisting bifurcations branches as well. This latter phenomenon induces multiple coexisting attractors consisting of two, three, four, five, or six disconnected symmetric or asymmetric attractors for the same set of parameter values when monitoring solely the initial conditions. Laboratory experimental measurements are carried out to confirm the theoretical predictions.