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

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

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FRACTIONAL DYNAMICS AT MULTIPLE TIMES.

Mark M Meerschaert¹, Peter Straka

¹Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, mcubed@unr.edu.

Journal of Statistical Physics

|February 5, 2013

Summary

This summary is machine-generated.

Continuous time random walks (CTRWs) introduce random waiting times and particle jumps. This study restores the Markov property using continuum renewal theory to compute joint CTRW densities.

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Area of Science:

* Physics
* Mathematics
* Stochastic Processes

Background:

* Continuous time random walks (CTRWs) model particle transport with random waiting times and jump lengths.
* Standard CTRW limits are non-Markovian, complicating process characterization despite solving fractional Fokker-Planck equations.

Purpose of the Study:

* To restore the Markovian property for CTRW processes.
* To compute the joint CTRW limit density at multiple time points.

Main Methods:

* Application of continuum renewal theory.
* Expansion of the state space to incorporate memory effects.
* Computation of joint probability densities.

Main Results:

* Successfully restored the Markov property on an expanded state space.
* Developed a method to compute the joint CTRW limit density across multiple times.

Conclusions:

* Continuum renewal theory provides a framework for analyzing non-Markovian CTRW processes.
* The methodology enables a more complete characterization of CTRW dynamics.