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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

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Transition to almost periodic patterns in circle map with delay: persistence as order parameter.

Bhagat Lal Dutta¹, Prashant M Gade

¹Centre for Modelling and Simulation, University of Pune, Pune 411007, India.

Chaos (Woodbury, N.Y.)

|October 5, 2013

Summary

This summary is machine-generated.

We investigated the delayed circle map using a spatiotemporal system analogy. Persistence acts as an order parameter, describing transitions between traveling and standing wave phases in this system.

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Area of Science:

Complex systems
Nonlinear dynamics
Chaos theory

Background:

The delayed circle map is a model system for studying complex dynamics.
An analogy exists between delayed maps and spatiotemporal systems, offering a new perspective.

Purpose of the Study:

To investigate the phases and transitions within the delayed circle map system.
To define and utilize an order parameter for phase transitions.

Main Methods:

Employing an analogy between the delayed circle map and spatiotemporal systems.
Analyzing the phase diagram to identify distinct phases (laminar, traveling defect, standing defect).
Defining and applying 'persistence' as an order parameter.

Main Results:

Observed distinct phases: laminar, traveling defect, and standing defect.
Identified 'persistence' as an effective order parameter for the traveling to standing wave phase transition.
Noted finite size scaling and off-critical scaling phenomena above the critical point.

Conclusions:

The spatiotemporal analogy provides a valuable framework for understanding the delayed circle map.
Persistence serves as a quantifiable measure for phase transitions in this pseudo-spatiotemporal system.
The system exhibits complex scaling behaviors near critical points.