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Abstract

Investigating on dynamics of Vibro-impact self sustained systems is a topic of great scientific interest, since systems which experience vibro-impact interactions can be found in different engineering applications. This paper proposes a study of coherence resonance, stochastic resonance and recurrence-based analysis in a time-delayed extended birhythmic self sustained vibro-impact system within enhanced memory damping regime under gaussian noise excitation input. Firstly, we obtain analytical approximate solutions with the help of non-smooth transformations, harmonic approximation and stochastic averaging method. The maximum extension of the pair of viscoelastic and time delay feedback parameters to have a birhythmic solution can be thus determined by an appropriated choice of the control parameter and restitution coefficient. Despite possible infinite variance characteristics of the noise term, the SR effect still occurs and can be detected by common quantifiers used in the studies of the phenomenon. The robustness of the SR is examined by use of standard measures within a continuous and a two-state description of the system. The system response is measured by inspection of the signal-to-noise ratio (SNR) and the spectral power amplification (SPA). The behavior of the SR quantifiers is typical, i.e. it is possible to find such a value of the noise intensity for which the SR phenomenon is observed and it is shown that this value is largely influenced by the system parameters. The results indicate that velocity and displacement feedback gains, time delay feedback settings, degree of energy loss during impact, and noise modulate the correlation from one stable state to another, impacting autocorrelation amplitude, spectral density, and creating a variation in the SNR. The paper provides substantial information about the numerical analysis and dynamical behavior of a multi limit cycle oscillator from the recurrence quantification analysis (RQA) perspective in the vibro-impact delayed system. By incorporating measures of complexity, determinism, laminarity, RQA can provide a more nuanced understanding of the underlying dynamics of complex nonlinear delayed system. The RQA parameters are used to discuss the birhythmic behavior of the vibro-impact system, as well as various bifurcations (quasi-periodicity, periodicity and chaos) in the system response.