Abstract
The stochastic resonance is investigated in the generalized Langevin equation with exponential memory kernel subjected to the joint action of internal noise, external noise and external sinusoidal forcing. The system is converted into three-dimensional Markovian Langevin equations. Furthermore, using the Shapiro-Loginov formula and the Laplace transformation technique, the exact expressions of the first moment and the steady response amplitude are obtained. The research results show that with the variations of external sinusoidal force frequency and the parameters of memory kernel and external noise, the system presents bona-fide stochastic resonance, conventional stochastic resonance and stochastic resonance in a broad sense under the condition of Routh-Hurwitz stability. In addition, the stochastic resonance can be weakened as the memory time increases. Moreover, the numerical results of power spectrum of system are in agreement with the analytic results.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
