The Analysis of Periodic Signal Detection Method Based on Duffing System Chaotic Dynamics

Chaos-based signal detection with discrete-time processing of the Duffing attractor

“…Dependence of the quantity L on amplitude of the useful signal A inf (Fig. 5) is similar in form to the dependence obtained in [23] by integration according to the A inf amplitude which confirms correctness of the performed calculations.…”

“…Accordingly, using sequences of types of dynamics 1-4 in time, it is possible to estimate and compare magnitudes of the shift of phase trajectories caused by influence of different forms of the input signal u(t) which is also confirmed by the results obtained in [23,24].…”

“…However, it should be noted that a same form of oscillation of the Duffing system can be obtained for different values of frequency ω 0 and amplitude A 0 when scaling coefficients are introduced into equation 2as shown in [23].…”

“…Structure of the Duffing attractor has properties of fractal geometry that manifest themselves in a connection with the homoclinic forms of phase trajectories. A more detailed analysis of the fractal geometry of the Duffing attractor is presented in [2,21,23] with schematic images.…”