Mixed-mode and chaotic oscillating circuits: Bifurcations and newtonian properties

We analyze properties of two singularly perturbed nonlinear systems with mixed-mode and chaotic oscillations and propose two op-amp RC circuits for the systems. The three-variable mathematical models of both systems (with cubic nonlinearities) are linked to the second Newton´s law d²x/dt² = F(t, x, dx/dt)/m, with F(t, x, dx/dt) containing a memory term. This allows further to use a scalar equation x´ = f(x)+ ∫y(τ; ∫z(θ; x)dθ)dτ as a base to design the circuits. The mixed-mode and chaotic responses as well as bifurcation diagrams of the circuits are obtained through Spice and Matlab simulations^.