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 |
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Keywords
- Chaos
- Complex systems
- Detailed balance
- Irreversible
- Non-equilibrium
ASJC Scopus subject areas
- Physics and Astronomy(all)
Cite this
Deciphering interactions of complex systems that do not satisfy detailed balance. / Nicholson, S. B.; Schulman, L. S.; Kim, Eun Jin.
In: Physics Letters, Section A: General, Atomic and Solid State Physics, Vol. 377, No. 31-33, 30.10.2013, p. 1810-1813.Research output: Contribution to journal › Article
}
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 -