Nonlinear Dynamics

, Volume 94, Issue 4, pp 2807–2825 | Cite as

Transition dynamics and adaptive synchronization of time-delay interconnected corticothalamic systems via nonlinear control

  • Denggui Fan
  • Liyuan Zhang
  • Qingyun WangEmail author
Original Paper


A modified corticothalamic (MCT) system with multiple delays for epileptic absence seizures is taken as a study object. Synchronization transition dynamics of two time-delay interconnected MCT systems via nonlinear control is investigated in this paper. Both the intrinsic delays in a single MCT system and the coupling delays between two MCT systems are considered. When there is no control, it is found that the occurrences of synchronization are dependent on the specific deviations of intrinsic delays and also correlated with the rhythmic periods of oscillations for the two MCT subsystems. To obtain the synchronous state transitions irrespective of the intrinsic delays, based on the Lyapunov stability theory, we propose a nonlinear adaptive control schemes with respect to the coupling delays. The numerical simulation results show the effectiveness of the designed control method.


Corticothalamic model Time delay Transition dynamics Adaptive synchronization Nonlinear control 



The authors gratefully acknowledge helpful comments by the potential reviewers and acknowledge support from the National Natural Science Foundation of China (Grant Nos. 11702018 and 11772019), the National Key R&D Program of China (Grant No. 2017YFF0207401), the Project funded by China Postdoctoral Science Foundation (Grant Nos. 2016M600037 and 2018T110043) and the Fundamental Research Funds for the Central Universities (FRF-TP-16-068A1).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of Mathematics and PhysicsUniversity of Science and Technology BeijingBeijingPeople’s Republic of China
  2. 2.Beijing Key Laboratory of Knowledge Engineering for Materials ScienceUniversity of Science and Technology BeijingBeijingPeople’s Republic of China
  3. 3.Department of Dynamics and ControlBeihang UniversityBeijingPeople’s Republic of China

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