Half-waves sequences technique for studying chaos in non-linear systems

Chaotic phenomena are studied by the half-waves sequences technique. Each time history is considered as an increasing and decreasing half-waves sequence, from which the half-periods, amplitudes and arithmetical mean values sequences are obtained. The procedure is applied to the second-order non-linear differential equations with sinusoidal forcing term, with particular attention to the cubic non-linearities of the Duffing-Ueda and van de Pol-Liénard equations. Many numerical results are developed and discussed, starting with Runge-Kutta integration.