Dynamical phases and phase transition in simplicially coupled logistic maps

Priyanka D. Bhoyar (), Naval R. Sabe and Prashant M. Gade
Additional contact information
Priyanka D. Bhoyar: Seth Kesarimal Porwal College of Arts and Science and Commerce, Kamptee 441 001, India
Naval R. Sabe: Department of Physics, Rashtrasant Tukadoji Maharaj Nagpur University, Nagpur 440 033, India
Prashant M. Gade: Department of Physics, Rashtrasant Tukadoji Maharaj Nagpur University, Nagpur 440 033, India

International Journal of Modern Physics C (IJMPC), 2025, vol. 36, issue 11, 1-14

Abstract: Coupled map lattices are a popular and computationally simpler model of pattern formation in nonlinear systems. In this work, we investigate three-site interactions with linear multiplicative coupling in one-dimensional coupled logistic maps that cannot be decomposed into pairwise interactions. We observe the transition to synchronization and the transition to long-range order in space. We coarse-grain the phase space in regions and denote them by spin values. We use two quantifiers the flip rate F(t) that quantify departure from expected band-periodicity as an order parameter. We also study a non-Markovian quantity, known as persistence P(t) to study dynamic phase transitions. Following transitions are observed. (a) Transition to two band attractor state: At this transition F(t) as well as P(t) shows a power-law decay in the range of coupling parameters. Here all sites reach one of the bands. The F(t) as well as P(t) decays as power-law with the decay exponent δ1=0.46 and η1=0.28, respectively. (b) The transition from a fluctuating chaotic state to a homogeneous synchronized fixed point: Here both the quantifiers F(t) and P(t) show power-law decay with decay exponent δ2=1 and η2=0.11, respectively. We compare the transitions with the case, where pairwise interactions are also present. The spatiotemporal evolution is analyzed as the coupling parameter is varied.

Keywords: Coupled map lattice; phase transitions; synchronization; logistic map; persistence; simplicial complex (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0129183125500172
Access to full text is restricted to subscribers

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:wsi:ijmpcx:v:36:y:2025:i:11:n:s0129183125500172

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0129183125500172

Access Statistics for this article

International Journal of Modern Physics C (IJMPC) is currently edited by H. J. Herrmann

More articles in International Journal of Modern Physics C (IJMPC) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().