The transition from solitons to chaos in the solution of the logistic equation (Q2710009)

The authors present a method for designing an electronic soliton generator. This generator is based on the circuit which can be described by the system (1): \(dx/dt = ax(1-x)\) and provides the derivative \(dx/dt (t)\) as output. In this case the output has ``impulse-like'' form \(c_1 \text{ sech}^2 (a(t+c_2)/2)\) with some constants \(c_1\) and \(c_2\). The authors also consider some dynamical properties of the Euler forward discretization for system (1). In particular, the period-doubling bifurcations and transition to chaos (numerically) are observed.