### Abstract

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

Pages (from-to) | 235-245 |

Number of pages | 11 |

Journal | Chaos, Solitons & Fractals |

Volume | 93 |

Early online date | 11 Nov 2016 |

DOIs | |

Publication status | Published - Dec 2016 |

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### Keywords

- Partial generalized synchronization
- Global generalized synchronization
- Structurally different time-delay systems
- Networks of time-delay systems

### Cite this

*Chaos, Solitons & Fractals*,

*93*, 235-245. https://doi.org/10.1016/j.chaos.2016.10.016

**Emergence of a common generalized synchronization manifold in network motifs of structurally different time-delay systems.** / Suresh, R.; Senthilkumar, D. V.; Lakshmanan, M.; Kurths, J.

Research output: Contribution to journal › Article

*Chaos, Solitons & Fractals*, vol. 93, pp. 235-245. https://doi.org/10.1016/j.chaos.2016.10.016

}

TY - JOUR

T1 - Emergence of a common generalized synchronization manifold in network motifs of structurally different time-delay systems

AU - Suresh, R.

AU - Senthilkumar, D. V.

AU - Lakshmanan, M.

AU - Kurths, J.

N1 - R. Suresh and D. V. Senthilkumar acknowledges the support from SERB-DST Fast Track scheme for Young Scientists. M. Lakshmanan (M. L.) has been supported by the DST, Government of India sponsored IRHPA research project. M. L. has also been supported by a DAE Raja Ramanna Fellowship.

PY - 2016/12

Y1 - 2016/12

N2 - We point out the existence of a transition from partial to global generalized synchronization (GS) in symmetrically coupled structurally different time-delay systems of different orders using the auxiliary system approach and the mutual false nearest neighbor method. The present authors have recently reported that there exists a common GS manifold even in an ensemble of structurally nonidentical scalar time-delay systems with different fractal dimensions and shown that GS occurs simultaneously with phase synchronization (PS). In this paper we confirm that the above result is not confined just to scalar one-dimensional time-delay systems alone but there exists a similar type of transition even in the case of time-delay systems with different orders. We calculate the maximal transverse Lyapunov exponent to evaluate the asymptotic stability of the complete synchronization manifold of each of the main and the corresponding auxiliary systems, which in turn ensures the stability of the GS manifold between the main systems. Further we estimate the correlation coefficient and the correlation of probability of recurrence to establish the relation between GS and PS. We also calculate the mutual false nearest neighbor parameter which doubly confirms the occurrence of the global GS manifold.

AB - We point out the existence of a transition from partial to global generalized synchronization (GS) in symmetrically coupled structurally different time-delay systems of different orders using the auxiliary system approach and the mutual false nearest neighbor method. The present authors have recently reported that there exists a common GS manifold even in an ensemble of structurally nonidentical scalar time-delay systems with different fractal dimensions and shown that GS occurs simultaneously with phase synchronization (PS). In this paper we confirm that the above result is not confined just to scalar one-dimensional time-delay systems alone but there exists a similar type of transition even in the case of time-delay systems with different orders. We calculate the maximal transverse Lyapunov exponent to evaluate the asymptotic stability of the complete synchronization manifold of each of the main and the corresponding auxiliary systems, which in turn ensures the stability of the GS manifold between the main systems. Further we estimate the correlation coefficient and the correlation of probability of recurrence to establish the relation between GS and PS. We also calculate the mutual false nearest neighbor parameter which doubly confirms the occurrence of the global GS manifold.

KW - Partial generalized synchronization

KW - Global generalized synchronization

KW - Structurally different time-delay systems

KW - Networks of time-delay systems

U2 - 10.1016/j.chaos.2016.10.016

DO - 10.1016/j.chaos.2016.10.016

M3 - Article

VL - 93

SP - 235

EP - 245

JO - Chaos, Solitons & Fractals

JF - Chaos, Solitons & Fractals

SN - 0960-0779

ER -