Chaotic Self-Oscillations in Autostochastic Systems with Smooth Multisegment Nonlinearity

A change in properties of chaotic oscillations in autonomous autostochastic systems of ordinary differential equations with multisegment nonlinearity is considered during smooth changeover from piecewise linear functions to the smooth dependences approximating them. Three types of smooth functions are given, which allow thepiecewise dependences to be approximated with an arbitrarily high accuracy. The absence of qualitative changes is noted in transfer from the piecewise nonlinear functions to their smooth analogs in autonomous autostochastic systems of ordinary differential equations. Variations in characteristics of motion occur gradually corresponding to the measure of deviation of a smooth approximating function from its piecewise linear prototype.