American Institute of Mathematical Sciences

Advanced
October  2001, 7(4): 737-745. doi: 10.3934/dcds.2001.7.737

Oscillation death in systems of oscillators with transferable coupling and time-delay

Ming He 1, , Xiaoyun Ma 2, and  Weijiang Zhang 1,

1. 

Department of Applied Mathematics, Shanghai Jiao Tong University, Shanghai, 200030, China, China
2. 

Mathematics/Computer Science Department, University of San Diego, San Diego, CA 92110, United States

Received  September 2000 Revised  May 2001 Published  July 2001

This paper addresses the oscillation death in systems of coupled neural oscillators. The coupling is assumed to be transferable and such transferable structure includes the nearest-neighbor coupling and the multiple-neighbor coupling. The death solution is obtained as a limit of upper solutions and lower solutions. We investigate a coupled cyclic chain of oscillators, in which the coupling is transferred in one direction and with a time lag. To obtain the asymptotic stability of the death solution, we establish the necessary and sufficient conditions to ensure the zeros for a class of exponential polynomials to lie to the left of the imaginary axis.
Keywords: Neural oscillator, exponential polynomial., oscillation death, transferability, stability, time delay.
Mathematics Subject Classification: 92C20, 3.
Citation: Ming He, Xiaoyun Ma, Weijiang Zhang. Oscillation death in systems of oscillators with transferable coupling and time-delay. Discrete and Continuous Dynamical Systems, 2001, 7 (4) : 737-745. doi: 10.3934/dcds.2001.7.737
[1]

Serge Nicaise, Cristina Pignotti, Julie Valein. Exponential stability of the wave equation with boundary time-varying delay. Discrete and Continuous Dynamical Systems - S, 2011, 4 (3) : 693-722. doi: 10.3934/dcdss.2011.4.693
[2]

Xiang Xie, Honglei Xu, Xinming Cheng, Yilun Yu. Improved results on exponential stability of discrete-time switched delay systems. Discrete and Continuous Dynamical Systems - B, 2017, 22 (1) : 199-208. doi: 10.3934/dcdsb.2017010
[3]

Ling Zhang, Xiaoqi Sun. Stability analysis of time-varying delay neural network for convex quadratic programming with equality constraints and inequality constraints. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022035
[4]

Quan Hai, Shutang Liu. Mean-square delay-distribution-dependent exponential synchronization of chaotic neural networks with mixed random time-varying delays and restricted disturbances. Discrete and Continuous Dynamical Systems - B, 2021, 26 (6) : 3097-3118. doi: 10.3934/dcdsb.2020221
[5]

Luis Barreira, Claudia Valls. Delay equations and nonuniform exponential stability. Discrete and Continuous Dynamical Systems - S, 2008, 1 (2) : 219-223. doi: 10.3934/dcdss.2008.1.219
[6]

Jing Li, Gui-Quan Sun, Zhen Jin. Interactions of time delay and spatial diffusion induce the periodic oscillation of the vegetation system. Discrete and Continuous Dynamical Systems - B, 2022, 27 (4) : 2147-2172. doi: 10.3934/dcdsb.2021127
[7]

Yaru Xie, Genqi Xu. Exponential stability of 1-d wave equation with the boundary time delay based on the interior control. Discrete and Continuous Dynamical Systems - S, 2017, 10 (3) : 557-579. doi: 10.3934/dcdss.2017028
[8]

Sylvia Novo, Rafael Obaya, Ana M. Sanz. Exponential stability in non-autonomous delayed equations with applications to neural networks. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 517-536. doi: 10.3934/dcds.2007.18.517
[9]

István Györi, Ferenc Hartung. Exponential stability of a state-dependent delay system. Discrete and Continuous Dynamical Systems, 2007, 18 (4) : 773-791. doi: 10.3934/dcds.2007.18.773
[10]

Farah Abdallah, Denis Mercier, Serge Nicaise. Spectral analysis and exponential or polynomial stability of some indefinite sign damped problems. Evolution Equations and Control Theory, 2013, 2 (1) : 1-33. doi: 10.3934/eect.2013.2.1
[11]

Alaa Hayek, Serge Nicaise, Zaynab Salloum, Ali Wehbe. Exponential and polynomial stability results for networks of elastic and thermo-elastic rods. Discrete and Continuous Dynamical Systems - S, 2022, 15 (5) : 1183-1220. doi: 10.3934/dcdss.2021142
[12]

Rui Hu, Yuan Yuan. Stability, bifurcation analysis in a neural network model with delay and diffusion. Conference Publications, 2009, 2009 (Special) : 367-376. doi: 10.3934/proc.2009.2009.367
[13]

Xiaochen Mao, Weijie Ding, Xiangyu Zhou, Song Wang, Xingyong Li. Complexity in time-delay networks of multiple interacting neural groups. Electronic Research Archive, 2021, 29 (5) : 2973-2985. doi: 10.3934/era.2021022
[14]

Tomás Caraballo, José Real, T. Taniguchi. The exponential stability of neutral stochastic delay partial differential equations. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 295-313. doi: 10.3934/dcds.2007.18.295
[15]

Linfang Liu, Tomás Caraballo, Xianlong Fu. Exponential stability of an incompressible non-Newtonian fluid with delay. Discrete and Continuous Dynamical Systems - B, 2018, 23 (10) : 4285-4303. doi: 10.3934/dcdsb.2018138
[16]

Ismael Maroto, Carmen Núñez, Rafael Obaya. Exponential stability for nonautonomous functional differential equations with state-dependent delay. Discrete and Continuous Dynamical Systems - B, 2017, 22 (8) : 3167-3197. doi: 10.3934/dcdsb.2017169
[17]

Xiong Li. The stability of the equilibrium for a perturbed asymmetric oscillator. Communications on Pure and Applied Analysis, 2006, 5 (3) : 515-528. doi: 10.3934/cpaa.2006.5.515
[18]

Xiong Li. The stability of the equilibrium for a perturbed asymmetric oscillator. Communications on Pure and Applied Analysis, 2007, 6 (1) : 69-82. doi: 10.3934/cpaa.2007.6.69
[19]

Cecilia Cavaterra, M. Grasselli. Robust exponential attractors for population dynamics models with infinite time delay. Discrete and Continuous Dynamical Systems - B, 2006, 6 (5) : 1051-1076. doi: 10.3934/dcdsb.2006.6.1051
[20]

Takeshi Taniguchi. The exponential behavior of Navier-Stokes equations with time delay external force. Discrete and Continuous Dynamical Systems, 2005, 12 (5) : 997-1018. doi: 10.3934/dcds.2005.12.997

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (69)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy