Dragon Intermittency at the Transition to Synchronization in Coupled Rulkov Neurons

Irina A. Bashkirtseva, Lev B. Ryashko and Alexander N. Pisarchik ()
Additional contact information
Irina A. Bashkirtseva: Institute of Mathematics and Computer Science, Ural Federal University, Lenina, 51, Ekaterinburg 620000, Russia
Lev B. Ryashko: Institute of Mathematics and Computer Science, Ural Federal University, Lenina, 51, Ekaterinburg 620000, Russia
Alexander N. Pisarchik: Center for Biomedical Technology, Universidad Politécnica de Madrid, Campus Montegancedo, Pozuelo de Alarcón, 28223 Madrid, Spain

Mathematics, 2025, vol. 13, issue 3, 1-15

Abstract: We investigate the synchronization dynamics of two non-identical, mutually coupled Rulkov neurons, emphasizing the effects of coupling strength and parameter mismatch on the system’s behavior. At low coupling strengths, the system exhibits multistability, characterized by the coexistence of three distinct 3-cycles. As the coupling strength is increased, the system becomes monostable with a single 3-cycle remaining as the sole attractor. A further increase in the coupling strength leads to chaos, which we identify as arising through a novel type of intermittency. This intermittency is characterized by alternating dynamics between two low-dimensional invariant subspaces: one corresponding to synchronization and the other to asynchronous behavior. We show that the system’s phase-space trajectory spends variable durations near one subspace before being repelled into the other, revealing non-trivial statistical properties near the onset of intermittency. Specifically, we find two key power-law scalings: (i) the mean duration of the synchronization interval scales with the coupling parameter, exhibiting a critical exponent of − 0.5 near the onset of intermittency, and (ii) the probability distribution of synchronization interval durations follows a power law with an exponent of − 1.7 for short synchronization intervals. Intriguingly, for each fixed coupling strength and parameter mismatch, there exists a most probable super-long synchronization interval, which decreases as either parameter is increased. We term this phenomenon “dragon intermittency” due to the distinctive dragon-like shape of the probability distribution of synchronization interval durations.

Keywords: Rulkov map; synchronization; chaos; intermittency; coupled system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/3/415/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/3/415/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:3:p:415-:d:1577952

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().