English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study the random processes with non-local memory and obtain new solutionsof the Mori-Zwanzig equation describing non-markovian systems. We analyze thesystem dynamics depending on the amplitudes $\nu$ and $\mu_0$ of the local andnon-local memory and pay attention to the line in the ($\nu$, $\mu_0$)-planeseparating the regions with asymptotically stationary and non-stationarybehavior. We obtain general equations for such boundaries and consider them forthree examples of the non-local memory functions. We show that there exist twotypes of the boundaries with fundamentally different system dynamics. On theboundaries of the first type, the diffusion with memory takes place, whereas onborderlines of the second type, the phenomenon of noise-induced resonance canbe observed. A distinctive feature of noise-induced resonance in the systemsunder consideration is that it occurs in the absence of an external regularperiodic force. It takes place due to the presence of frequencies in the noisespectrum, which are close to the self-frequency of the system. We analyze alsothe variance of the process and compare its behavior for regions of asymptoticstationarity and non-stationarity, as well as for diffusive andnoise-induced-resonance borderlines between them.

Memory-dependent noise-induced resonance and diffusion in non-markovian systems