### Abstract

We present an extension of a novel method for understanding complex systems, which has been applied to non-equilibrium systems both in and out of detailed balance. For the non-detailed balance case, in which non-zero currents are a principal indicator of complexity, there has been an incomplete understanding of the distance function in the observable representation embedding. To deal with this we construct a new transition matrix by accounting for this current and compute the eigenvalues and eigenvectors. From these, we define a metric whose distance provides a useful measure of the relation among variables. Use of this method provides insights into long-range correlation, and chaotic properties. As an example we show that these distances can be used to control chaos in a simple dynamical system.

Original language | English |
---|---|

Pages (from-to) | 1810-1813 |

Number of pages | 4 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 377 |

Issue number | 31-33 |

Early online date | 22 May 2013 |

DOIs | |

Publication status | Published - 30 Oct 2013 |

Externally published | Yes |

### Fingerprint

### Keywords

- Chaos
- Complex systems
- Detailed balance
- Irreversible
- Non-equilibrium

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physics Letters, Section A: General, Atomic and Solid State Physics*,

*377*(31-33), 1810-1813. https://doi.org/10.1016/j.physleta.2013.05.036

**Deciphering interactions of complex systems that do not satisfy detailed balance.** / Nicholson, S. B.; Schulman, L. S.; Kim, Eun Jin.

Research output: Contribution to journal › Article

*Physics Letters, Section A: General, Atomic and Solid State Physics*, vol. 377, no. 31-33, pp. 1810-1813. https://doi.org/10.1016/j.physleta.2013.05.036

}

TY - JOUR

T1 - Deciphering interactions of complex systems that do not satisfy detailed balance

AU - Nicholson, S. B.

AU - Schulman, L. S.

AU - Kim, Eun Jin

PY - 2013/10/30

Y1 - 2013/10/30

N2 - We present an extension of a novel method for understanding complex systems, which has been applied to non-equilibrium systems both in and out of detailed balance. For the non-detailed balance case, in which non-zero currents are a principal indicator of complexity, there has been an incomplete understanding of the distance function in the observable representation embedding. To deal with this we construct a new transition matrix by accounting for this current and compute the eigenvalues and eigenvectors. From these, we define a metric whose distance provides a useful measure of the relation among variables. Use of this method provides insights into long-range correlation, and chaotic properties. As an example we show that these distances can be used to control chaos in a simple dynamical system.

AB - We present an extension of a novel method for understanding complex systems, which has been applied to non-equilibrium systems both in and out of detailed balance. For the non-detailed balance case, in which non-zero currents are a principal indicator of complexity, there has been an incomplete understanding of the distance function in the observable representation embedding. To deal with this we construct a new transition matrix by accounting for this current and compute the eigenvalues and eigenvectors. From these, we define a metric whose distance provides a useful measure of the relation among variables. Use of this method provides insights into long-range correlation, and chaotic properties. As an example we show that these distances can be used to control chaos in a simple dynamical system.

KW - Chaos

KW - Complex systems

KW - Detailed balance

KW - Irreversible

KW - Non-equilibrium

UR - http://www.scopus.com/inward/record.url?scp=84878867610&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2013.05.036

DO - 10.1016/j.physleta.2013.05.036

M3 - Article

VL - 377

SP - 1810

EP - 1813

JO - Physics Letters A

JF - Physics Letters A

SN - 0375-9601

IS - 31-33

ER -