Stability of synchronization manifolds and its nonlinear behaviour in memristive coupled discrete neuron model

Anwar MS, Ghosh D (2022) Stability of synchronization in simplicial complexes with multiple interaction layers. Phys Rev E 106(3):034314. https://doi.org/10.1103/PhysRevE.106.034314

Article  CAS  PubMed  Google Scholar 

Banerjee R, Bera BK, Ghosh D et al (2017) Enhancing synchronization in chaotic oscillators by induced heterogeneity. Eur Phys J Spec Top 226:1893–1902. https://doi.org/10.1140/epjst/e2017-70027-9

Article  Google Scholar 

Baysal V, Saraç Z, Yilmaz E (2019) Chaotic resonance in Hodgkin–Huxley neuron. Nonlinear Dyn 97:1275–1285. https://doi.org/10.1007/s11071-019-05047-w

Article  Google Scholar 

Baysal V, Solmaz R, Ma J (2023) Investigation of chaotic resonance in Type-I and Type-II Morris–Lecar neurons. Appl Math Comput 448:127940. https://doi.org/10.1016/j.amc.2023.127940

Article  Google Scholar 

Belykh IV, Belykh VN, Hasler M (2004) Blinking model and synchronization in small-world networks with a time-varying coupling. Physica D 195(1–2):188–206. https://doi.org/10.1016/j.physd.2004.03.013

Article  Google Scholar 

Belykh I, De Lange E, Hasler M (2005) Synchronization of bursting neurons: what matters in the network topology. Phys Rev Lett 94(18):188101. https://doi.org/10.1103/PhysRevLett.94.188101

Article  CAS  PubMed  Google Scholar 

Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang DU (2006) Complex networks: structure and dynamics. Phys Rep 424(4–5):175–308. https://doi.org/10.1016/j.physrep.2005.10.009

Article  Google Scholar 

Budzinski RC, Boaretto BRR, Prado TL, Lopes SR (2019) Phase synchronization and intermittent behavior in healthy and Alzheimer-affected human-brain-based neural network. Phys Rev E 99(2–1):022402. https://doi.org/10.1103/physreve.99.022402

Article  CAS  PubMed  Google Scholar 

Calim A, Baysal V (2023) Chaotic resonance in an astrocyte-coupled excitable neuron. Chaos Soliton Fract 176:114105. https://doi.org/10.1016/j.chaos.2023.114105

Article  Google Scholar 

Dahms T, Lehnert J, Schöll E (2012) Cluster and group synchronization in delay-coupled networks. Phys Rev E 86(1):016202. https://doi.org/10.1103/PhysRevE.86.016202

Article  CAS  Google Scholar 

Fang X, Duan S, Wang L (2023) Memristive FHN spiking neuron model and brain-inspired threshold logic computing. Neurocomputing 517:93–105. https://doi.org/10.1016/j.neucom.2022.08.056

Article  Google Scholar 

FitzHugh R (1955) Mathematical models of threshold phenomena in the nerve membrane. Bull Math Biophys 17:257–278. https://doi.org/10.1007/BF02477753

Article  Google Scholar 

FitzHugh R (1961) Impulses and physiological states in theoretical models of nerve membrane. Biophys J 1(6):445–466. https://doi.org/10.1016/S0006-3495(61)86902-6

Article  CAS  PubMed  PubMed Central  Google Scholar 

FitzHugh R (1969) Mathematical models of excitation and propagation in nerve. Biological engineering. McGraw-Hill Book Co., New York, pp 1–85

Google Scholar 

Gambuzza LV, Di Patti F, Gallo L, Lepri S, Romance M, Criado R, Frasca M, Latora V, Boccaletti S (2021) Stability of synchronization in simplicial complexes. Nat Commun 12(1):1255. https://doi.org/10.1038/s41467-021-21486-9

Article  CAS  PubMed  PubMed Central  Google Scholar 

Gerster M, Berner R, Sawicki J, Zakharova A, Škoch A, Hlinka J, Lehnertz K, Schöll E (2020) FitzHugh–Nagumo oscillators on complex networks mimic epileptic–seizure-related synchronization phenomena. Chaos 30:123130. https://doi.org/10.1063/5.0021420

Article  PubMed  Google Scholar 

Huang L, Chen Q, Lai YC, Pecora LM (2009) Generic behavior of master-stability functions in coupled nonlinear dynamical systems. Phys Rev E 80(3):036204. https://doi.org/10.1103/physreve.80.036204

Article  Google Scholar 

Izhikevich EM (2007) Dynamical systems in neuroscience. MIT Press, Cambridge

Google Scholar 

Kumarasamy S, Srinivasan A, Ramasamy M, Rajagopal K (2022) Strange nonchaotic dynamics in a discrete FitzHugh–Nagumo neuron model with sigmoidal recovery variable. Chaos 32(7):073106. https://doi.org/10.1063/5.0089373

Article  PubMed  Google Scholar 

Kumarasamy S, Moroz IM, Sampathkumar SK, Karthikeyan A, Karthikeyan R (2023) Dynamics and network behavior of a four-dimensional discrete neuron model with magnetic flux coupling. Eur Phys J Plus 138:683. https://doi.org/10.1140/epjp/s13360-023-04329-y

Article  Google Scholar 

Lehnertz K, Bialonski S, Horstmann MT, Krug D, Rothkegel A, Staniek M, Wagner T (2009) Synchronization phenomena in human epileptic brain networks. J Neurosci Methods 183(1):42–48. https://doi.org/10.1016/j.jneumeth.2009.05.015

Article  PubMed  Google Scholar 

Li Y, Lv M, Ma J, Hu X (2024) A discrete memristive neuron and its adaptive dynamics. Nonlinear Dyn 112:7541–7553. https://doi.org/10.1007/s11071-024-09361-w

Article  Google Scholar 

Ma J (2024) Energy function for some maps and nonlinear oscillators. Appl Math Comput 463:128379. https://doi.org/10.1016/j.amc.2023.128379

Article  Google Scholar 

Majhi S, Bera B, Banerjee S et al (2016) Synchronization of chaotic modulated time delay networks in presence of noise. Eur Phys J Spec Top 225:65–74. https://doi.org/10.1140/epjst/e2016-02624-9

Article  Google Scholar 

Nagumo J, Arimoto S, Yoshizawa S (1962) An active pulse transmission line simulating nerve axon. Proc IRE 50(10):2061–2070. https://doi.org/10.1109/JRPROC.1962.288235

Article  Google Scholar 

Nishikawa T, Motter AE (2010) Network synchronization landscape reveals compensatory structures, quantization, and the positive effect of negative interactions. PNAS 107(23):10342–10347. https://doi.org/10.1073/pnas.0912444107

Article  PubMed  PubMed Central  Google Scholar 

Parastesh F, Azarnoush H, Jafari S, Hatef B, Perc M, Repnik R (2019) Synchronizability of two neurons with switching in the coupling. Appl Math Comput 350:217–223. https://doi.org/10.1016/j.amc.2019.01.011

Article  Google Scholar 

Parastesh F, Jafari S, Azarnoush H, Shahriari Z, Wang Z, Boccaletti S, Perc M (2021) Chimeras. Phys Rep 898:1–114. https://doi.org/10.1016/j.physrep.2020.10.003

Article  Google Scholar 

Pecora LM, Carroll TL (1998) Master stability functions for synchronized coupled systems. Phys Rev Lett 80(10):2109. https://doi.org/10.1103/PhysRevLett.80.2109

Article  CAS  Google Scholar 

Rajagopal K, Jafari S, Moroz I, Karthikeyan A, Srinivasan A (2021) Noise induced suppression of spiral waves in a hybrid FitzHugh–Nagumo neuron with discontinuous resetting. Chaos 31(7):073117. https://doi.org/10.1063/5.0059175

Article  PubMed  Google Scholar 

Rakshit S, Bera BK, Ghosh D, Sinha S (2018) Emergence of synchronization and regularity in firing patterns in time-varying neural hypernetworks. Phys Rev E 97(5):052304. https://doi.org/10.1103/PhysRevE.97.052304

Article  PubMed  Google Scholar 

Ramadoss J, Rajagopal K, Natiq H, Hussain I (2022) The linearity of the master stability function. EPL 139(1):12002. https://doi.org/10.1209/0295-5075/ac4199

Article  CAS  Google Scholar 

Ramasamy M, Rajagopal K, Ramakrishnan B, Karthikeyan A (2023) Effect of external excitation on synchronization behavior in a network of neuron models. Physica A 625:129032. https://doi.org/10.1016/j.physa.2023.129032

Article  Google Scholar 

Ramasamy M, Kumarasamy S, Sampathkumar SK, Karthikeyan A, Rajagopal K (2023a) Synchronizability of discrete nonlinear systems: a master stability function approach. Complexity 1:6616560. https://doi.org/10.1155/2023/6616560

Article  Google Scholar 

Sun X, Lei J, Perc M, Kurths J, Chen G (2011) Burst synchronization transitions in a neuronal network of subnetworks. Chaos 21:016110. https://doi.org/10.1063/1.3559136

Article  PubMed  Google Scholar 

Tang L, Wu X, Lü J, Lu JA, D’Souza RM (2019) Master stability functions for complete, intralayer, and interlayer synchronization in multiplex networks of coupled Rössler oscillators. Phys Rev E 99(1):012304. https://doi.org/10.1103/PhysRevE.99.012304

Article  CAS  PubMed 

Comments (0)

No login
gif