Sufficient synchronization conditions for resistively and memristively coupled oscillators of FitzHugh-Nagumo-type
Tóm tắt
We study the synchronization behavior of a class of identical FitzHugh-Nagumo-type oscillators under adaptive coupling. We describe the oscillators by a circuit model and we provide a sufficient synchronization condition that relies on the shape of the nonlinear conductance’s (
Từ khóa
Tài liệu tham khảo
Abernot M, Gil T, Jiménez M, Núñez J, Avellido MJ, Linares-Barranco B, Gonos T, Hardelin T, Todri-Sanial A. Digital implementation of oscillatory neural network for image recognition applications. Front Neurosci. 2021. https://doi.org/10.3389/fnins.2021.713054.
Ahmed I, Chiu PW, Moy W, Kim CH. A probabilistic compute fabric based on coupled ring oscillators for solving combinatorial optimization problems. IEEE J Solid State Circuits. 2021;56(9):2870–80. https://doi.org/10.1109/JSSC.2021.3062821.
Aminzare Z, Dey B, Davison EN, Leonard NE. Cluster synchronization of diffusively coupled nonlinear systems: A contraction-based approach. J Nonlinear Sci. 2020. https://doi.org/10.1007/s00332-018-9457-y.
Aminzare Z, Sontag E. Synchronization of diffusively-connected nonlinear systems: Results based on contractions with respect to general norms. IEEE Trans Netw Sci Eng. 2014;1:91–106.
Aminzare Z, Srivastava V. Stochastic synchronization in nonlinear network systems driven by intrinsic and coupling noise. Biol Cybern. 2022. https://doi.org/10.1007/s00422-022-00928-7.
Arbib M, Amari S, Arbib P. The handbook of brain theory and neural networks. A Bradford book. Cambridge: MIT Press; 2003.
Barbalat I. Systems d’equations differentielles d’oscillations nonlinéaires. Revue Roumaine Math Pures Appl. 1959;4:267–70.
Biggs N. Algebraic graph theory, 2 edn. Cambridge Mathematical Library. Cambridge University Press; 1974. https://doi.org/10.1017/CBO9780511608704
Bullo F. Contraction theory for dynamical systems, 1.1 edn. Kindle Direct Publishing; 2023. https://fbullo.github.io/ctds
Chou J, Bramhavar S, Ghosh S, Herzog W. Analog coupled oscillator based weighted ising machine. Sci Rep. 2019;9(1):14786. https://doi.org/10.1038/s41598-019-49699-5.
Chua L. Memristor-the missing circuit element. IEEE Trans Circuits Theor. 1971;18(5):507–19. https://doi.org/10.1109/TCT.1971.1083337.
Chua L, Kang SM. Memristive devices and systems. Proc IEEE. 1976;64(2):209–23. https://doi.org/10.1109/PROC.1976.10092.
Csaba G, Porod W. Coupled oscillators for computing: A review and perspective. Appl Phys Rev. 2020;7(1). https://doi.org/10.1063/1.5120412.
Davison EN, Dey B, Leonard NE. Synchronization bound for networks of nonlinear oscillators. In: 2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2016; pp. 1110–1115. https://doi.org/10.1109/ALLERTON.2016.7852359
DeLellis P, diBernardo M, Garofalo F. Synchronization of complex networks through local adaptive coupling. Chaos Interdiscip J Nonlinear Sci. 2008;18(3): 037110. https://doi.org/10.1063/1.2944236.
DeLellis P, diBernardo M, Garofalo F. Decentralized adaptive control for synchronization and consensus of complex networks, pp. 27–42. Springer Berlin Heidelberg, Berlin, Heidelberg; 2009. https://doi.org/10.1007/978-3-642-03199-1_2.
Delellis P, Di Bernardo M, Russo G. On quad, lipschitz, and contracting vector fields for consensus and synchronization of networks. Circ Syst I: Regul Papers, IEEE Trans. 2011;58:576–83. https://doi.org/10.1109/TCSI.2010.2072270.
DeLellis P, diBernardo M, Garofalo F. Novel decentralized adaptive strategies for the synchronization of complex networks. Automatica. 2009;45(5):1312–8. https://doi.org/10.1016/j.automatica.2009.01.001.
Demidovic BP. Dissipativity of a nonlinear system of differential equations. Uspekhi Matematicheskikh Nauk. 1961;16:216.
Dörfler F, Bullo F. On the critical coupling for kuramoto oscillators. SIAM J Appl Dyn Syst. 2011;10(3):1070–99. https://doi.org/10.1137/10081530X.
Dörfler F, Bullo F. Synchronization in complex networks of phase oscillators: a survey. Automatica. 2014. https://doi.org/10.1016/j.automatica.2014.04.012.
Duan S, Hu X, Dong Z, Wang L, Mazumder P. Memristor-based cellular nonlinear/neural network: design, analysis, and applications. IEEE Trans Neural Netw Learn Syst. 2015;26(6):1202–13. https://doi.org/10.1109/TNNLS.2014.2334701.
Feketa P, Schaum A, Meurer T. Synchronization and multicluster capabilities of oscillatory networks with adaptive coupling. IEEE Trans Autom Control. 2021;66(7):3084–96. https://doi.org/10.1109/TAC.2020.3012528.
FitzHugh R. Impulses and physiological states in theoretical models of nerve membrane. Biophys J. 1961;1(6):445–66. https://doi.org/10.1016/S0006-3495(61)86902-6.
Ignatov M, Hansen M, Ziegler M, Kohlstedt H. Synchronization of two memristively coupled van der Pol oscillators. Appl Phys Lett. 2016;108(8). https://doi.org/10.1063/1.4942832.
Jafarpour S, Cisneros-Velarde P, Bullo F. Weak and semi-contraction for network systems and diffusively coupled oscillators. IEEE Trans Autom Control. 2022;67(3):1285–300. https://doi.org/10.1109/TAC.2021.3073096.
Jafarpour S, Davydov A, Bullo F. Non-euclidean contraction theory for monotone and positive systems. IEEE Trans Autom Control. 2023;68(9):5653–60. https://doi.org/10.1109/TAC.2022.3224094.
Jin X, Wu YG, Lü HP, Xu C. Synchronization dynamics of phase oscillators with generic adaptive coupling. Commun Theor Phys. 2023;75(4). https://doi.org/10.1088/1572-9494/acba84.
Johnson AP, Liu J, Millard AG, Karim S, Tyrrell AM, Harkin J, Timmis J, McDaid LJ, Halliday DM. Homeostatic fault tolerance in spiking neural networks: A dynamic hardware perspective. IEEE Trans Circuits Syst I Regul Pap. 2018;65(2):687–99. https://doi.org/10.1109/TCSI.2017.2726763.
Joshi SK, Sen S, Kar IN. Synchronization of coupled benchmark oscillators: analysis and experiments. Int J Dyn Control. 2022;10:577–97. https://doi.org/10.1007/s40435-021-00827-y.
Korneev I, Semenov V, Vadivasova T. Synchronization of periodic self-oscillators interacting via memristor-based coupling. Int J Bifurc Chaos. 2020;30:2050096. https://doi.org/10.1142/S0218127420500960.
Korneev IA, Ramazanov IR, Semenov VV, Slepnev AV, Vadivasova TE. Synchronization of traveling waves in memristively coupled ensembles of fitzhugh-nagumo neurons with periodic boundary conditions. Frontiers in Physics. 2022. https://doi.org/10.3389/fphy.2022.886476.
Li H, Fang JA, Li X, Rutkowski L, Huang T. Event-triggered synchronization of multiple discrete-time markovian jump memristor- based neural networks with mixed mode-dependent delays. IEEE Trans Circuits Syst I Regul Pap. 2022;69(5):2095–107. https://doi.org/10.1109/TCSI.2022.3149535.
Li M, Hong Q, Wang X. Memristor-based circuit implementation of competitive neural network based on online unsupervised hebbian learning rule for pattern recognition. Neural Comput Appl. 2022;34(1):319–31. https://doi.org/10.1007/s00521-021-06361-4.
Ma J, Xu W, Zhou P, Zhang G. Synchronization between memristive and initial-dependent oscillators driven by noise. Phys A Stat Mech Appl. 2019;536:122598. https://doi.org/10.1016/j.physa.2019.122598
Michaelis D, Ochs K, Jenderny S. A memristive circuit for gait pattern classification based on self-organized axon growth. In: 2021 IEEE International Midwest Symposium on Circuits and Systems (MWSCAS), pp. 162–165. 2021. https://doi.org/10.1109/MWSCAS47672.2021.9531806
Nagumo J, Arimoto S, Yoshizawa S. An active pulse transmission line simulating nerve axon. Proc IRE. 1962;50(10):2061–70. https://doi.org/10.1109/JRPROC.1962.288235.
Ndow FK, Aminzare Z. Global synchronization analysis of non-diffusively coupled networks through contraction theory (2023). Preprint, https://arxiv.org/abs/2307.00030
Ochs K, AlBeattie B, Jenderny S. An ising machine solving max-cut problems based on the circuit synthesis of the phase dynamics of a modified kuramoto model. In: 2021 IEEE International Midwest Symposium on Circuits and Systems (MWSCAS), pp. 982–985 (2021). https://doi.org/10.1109/MWSCAS47672.2021.9531734
Ochs K, Michaelis D, Jenderny S. Synthesis of an equivalent circuit for spike-timing-dependent axon growth: What fires together now really wires together. IEEE Trans Circuits Syst I Regul Pap. 2021;68(9): 3656–3667. https://doi.org/10.1109/TCSI.2021.3093172
Ochs K, Michaelis D, Solan E, Feketa P, Schaum A, Meurer T. Synthesis, design, and synchronization analysis of coupled linear electrical networks. IEEE Trans Circuits Syst I Regul Pap. 2020;67(12):4521–32. https://doi.org/10.1109/TCSI.2020.3002672.
Pecora LM, Carroll TL. Master stability functions for synchronized coupled systems. Phys Rev Lett. 1998;80:2109–12. https://doi.org/10.1103/PhysRevLett.80.2109.
Petrovas A, Lisauskas S, Slepikas A. Electronic model of fitzhugh-nagumo neuron. Elektronika ir Elektrotechnika. 2012;122(6):117–20. https://doi.org/10.5755/j01.eee.122.6.1835. https://eejournal.ktu.lt/index.php/elt/article/view/1835
Pogromsky A, Glad T, Nijmeijer H. On diffusion driven oscillations in coupled dynamical systems. International Journal of Bifurcation and Chaos. 1999;9:629–44. https://doi.org/10.1142/S0218127499000444.
Ringkvist M, Zhou Y. On the dynamical behaviour of fitzhugh-nagumo systems: revisited. Nonlinear Anal Theory Methods Appl Nonlinear Anal-Theor Meth APP. 2009;71:2667–87. https://doi.org/10.1016/j.na.2009.01.149.
Steur E, Tyukin IY, Nijmeijer H. Semi-passivity and synchronization of diffusively coupled neuronal oscillators. Physica D. 2009;238:2119–28.
Strukov DB, Snider GS, Stewart DR, Williams RS. The missing memristor found. Nature. 2008;453:80–3. https://doi.org/10.1038/nature06932.
Sun Z. A gathering of barbalat’s lemmas and their (unsung) cousins. 2023. https://doi.org/10.48550/arXiv.2301.00466
Tao G. A simple alternative to the barbalat lemma. IEEE Trans Autom Control. 1997;42(5):698. https://doi.org/10.1109/9.580878.
Wang C, Lv M, Alsaedi A, Ma J. Synchronization stability and pattern selection in a memristive neuronal network. Chaos Interdiscipl J Nonlinear Sci. 2017;27(11):113108. https://doi.org/10.1063/1.5004234.
Wang X, Zheng Z, Xu C. Explosive synchronization in phase oscillator populations with attractive and repulsive adaptive interactions. Chaos, Solitons Fractals. 2023;170: 113351.https://doi.org/10.1016/j.chaos.2023.113351. www.sciencedirect.com/science/article/pii/S0960077923002527
Willems JC. Dissipative dynamical systems part I: general theory. Arch Ration Mech Anal. 1972;45(5):321–51. https://doi.org/10.1007/BF00276493.
Wu CW, Chua L. Synchronization in an array of linearly coupled dynamical systems. IEEE Trans Circ Syst I: Fundam Theory and Appl. 1995;42(8):430–47. https://doi.org/10.1109/81.404047.