October  2000, 6(4): 841-860. doi: 10.3934/dcds.2000.6.841

Neuronal dynamics in time varying enviroments: Continuous and discrete time models

1. 

School of Informatics and Engineering, Flinders University of South Australia, Bedford Park SA 5042, Australia, Australia

Received  May 1999 Revised  May 2000 Published  August 2000

The convergence characteristics of an isolated Hopfield-type neuron in time varying environments are considered in particular when the neuronal parameters are assumed to be almost periodic. This study includes the investigations of neurons having periodic parameters but the periods are not integrally dependent. Both continuous-time-continuous-state and discrete-time-continuous-state models are discussed. Sufficient conditions are established for associative stimulus. It is shown that when the nreronal gain is dominated by the neuronal dissipation on average, associative recall of the encoded temporal pattern is guaranteed and this is achieved by the global stability of the encoded pattern.
Citation: S. Mohamad, K. Gopalsamy. Neuronal dynamics in time varying enviroments: Continuous and discrete time models. Discrete and Continuous Dynamical Systems, 2000, 6 (4) : 841-860. doi: 10.3934/dcds.2000.6.841
[1]

Ferenc A. Bartha, Ábel Garab. Necessary and sufficient condition for the global stability of a delayed discrete-time single neuron model. Journal of Computational Dynamics, 2014, 1 (2) : 213-232. doi: 10.3934/jcd.2014.1.213

[2]

Ran Dong, Xuerong Mao. Asymptotic stabilization of continuous-time periodic stochastic systems by feedback control based on periodic discrete-time observations. Mathematical Control and Related Fields, 2020, 10 (4) : 715-734. doi: 10.3934/mcrf.2020017

[3]

Willem Mélange, Herwig Bruneel, Bart Steyaert, Dieter Claeys, Joris Walraevens. A continuous-time queueing model with class clustering and global FCFS service discipline. Journal of Industrial and Management Optimization, 2014, 10 (1) : 193-206. doi: 10.3934/jimo.2014.10.193

[4]

J. C. Dallon, Lynnae C. Despain, Emily J. Evans, Christopher P. Grant. A continuous-time stochastic model of cell motion in the presence of a chemoattractant. Discrete and Continuous Dynamical Systems - B, 2020, 25 (12) : 4839-4852. doi: 10.3934/dcdsb.2020129

[5]

Hui Meng, Fei Lung Yuen, Tak Kuen Siu, Hailiang Yang. Optimal portfolio in a continuous-time self-exciting threshold model. Journal of Industrial and Management Optimization, 2013, 9 (2) : 487-504. doi: 10.3934/jimo.2013.9.487

[6]

Andy Hammerlindl, Bernd Krauskopf, Gemma Mason, Hinke M. Osinga. Determining the global manifold structure of a continuous-time heterodimensional cycle. Journal of Computational Dynamics, 2022, 9 (3) : 393-419. doi: 10.3934/jcd.2022008

[7]

Eduardo Liz. A new flexible discrete-time model for stable populations. Discrete and Continuous Dynamical Systems - B, 2018, 23 (6) : 2487-2498. doi: 10.3934/dcdsb.2018066

[8]

Ming Chen, Hao Wang. Dynamics of a discrete-time stoichiometric optimal foraging model. Discrete and Continuous Dynamical Systems - B, 2021, 26 (1) : 107-120. doi: 10.3934/dcdsb.2020264

[9]

H. L. Smith, X. Q. Zhao. Competitive exclusion in a discrete-time, size-structured chemostat model. Discrete and Continuous Dynamical Systems - B, 2001, 1 (2) : 183-191. doi: 10.3934/dcdsb.2001.1.183

[10]

Cuicui Li, Lin Zhou, Zhidong Teng, Buyu Wen. The threshold dynamics of a discrete-time echinococcosis transmission model. Discrete and Continuous Dynamical Systems - B, 2021, 26 (10) : 5197-5216. doi: 10.3934/dcdsb.2020339

[11]

Ziyad AlSharawi, Nikhil Pal, Joydev Chattopadhyay. The role of vigilance on a discrete-time predator-prey model. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022017

[12]

Ming-Zhen Xin, Bin-Guo Wang. Spatial dynamics of an epidemic model in time almost periodic and space periodic media. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022116

[13]

Denis Pennequin. Existence of almost periodic solutions of discrete time equations. Discrete and Continuous Dynamical Systems, 2001, 7 (1) : 51-60. doi: 10.3934/dcds.2001.7.51

[14]

Lakhdar Aggoun, Lakdere Benkherouf. A Markov modulated continuous-time capture-recapture population estimation model. Discrete and Continuous Dynamical Systems - B, 2005, 5 (4) : 1057-1075. doi: 10.3934/dcdsb.2005.5.1057

[15]

Lizhong Qiang, Bin-Guo Wang. An almost periodic malaria transmission model with time-delayed input of vector. Discrete and Continuous Dynamical Systems - B, 2017, 22 (4) : 1525-1546. doi: 10.3934/dcdsb.2017073

[16]

Huijuan Li, Junxia Wang. Input-to-state stability of continuous-time systems via finite-time Lyapunov functions. Discrete and Continuous Dynamical Systems - B, 2020, 25 (3) : 841-857. doi: 10.3934/dcdsb.2019192

[17]

Joon Kwon, Panayotis Mertikopoulos. A continuous-time approach to online optimization. Journal of Dynamics and Games, 2017, 4 (2) : 125-148. doi: 10.3934/jdg.2017008

[18]

Hanqing Jin, Xun Yu Zhou. Continuous-time portfolio selection under ambiguity. Mathematical Control and Related Fields, 2015, 5 (3) : 475-488. doi: 10.3934/mcrf.2015.5.475

[19]

Zhigang Zeng, Tingwen Huang. New passivity analysis of continuous-time recurrent neural networks with multiple discrete delays. Journal of Industrial and Management Optimization, 2011, 7 (2) : 283-289. doi: 10.3934/jimo.2011.7.283

[20]

Vladimir Răsvan. On the central stability zone for linear discrete-time Hamiltonian systems. Conference Publications, 2003, 2003 (Special) : 734-741. doi: 10.3934/proc.2003.2003.734

2021 Impact Factor: 1.588

Metrics

  • PDF downloads (108)
  • HTML views (0)
  • Cited by (17)

Other articles
by authors

[Back to Top]