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Transition to period-3 synchronized state in coupled gauss maps
Pratik M Gaiki1, Ankosh D Deshmukh2, Sumit S Pakhare3
1Department of Physics, Shri Shivaji Education Society Amravati's, Shri Shivaji Arts, Commerce & Science College, Motala 443103, Buldana District, Maharashtra, India.
Chaos (Woodbury, N.Y.)
|February 16, 2024
Summary
Researchers studied coupled Gauss maps, observing transitions from chaos to period-3 states. They identified a new universality class for synchronized period-3 states, a rare phenomenon in one dimension.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Statistical Physics
Background:
- Coupled map lattices are used to model complex spatio-temporal phenomena.
- Synchronized periodic states are rare in one-dimensional systems due to defect formation.
Purpose of the Study:
- To investigate transitions in one-dimensional coupled Gauss maps.
- To characterize synchronized period-3 states and their universality class.
Main Methods:
- Analysis of coupled Gauss maps with nearest-neighbor interactions.
- Definition and use of an order parameter based on site states relative to a fixed point.
- Characterization of transitions using universality classes and finite-size scaling.
Main Results:
- Observed transitions from spatiotemporal chaos to coarse-grained period-3 states.
- Identified three distinct transition types: directed-percolation, Ising-type, and a novel synchronized period-3 state.
- Finite-size scaling analysis suggests the synchronized period-3 transition belongs to a new universality class.
Conclusions:
- One-dimensional coupled Gauss maps exhibit rich transition dynamics.
- A rare synchronized period-3 state has been identified and characterized.
- The findings suggest the existence of a new universality class for synchronized periodic behavior in 1D systems.
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