Papers
Topics
Authors
Recent
Assistant
AI Research Assistant
Well-researched responses based on relevant abstracts and paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses.
Gemini 2.5 Flash
Gemini 2.5 Flash 194 tok/s
Gemini 2.5 Pro 47 tok/s Pro
GPT-5 Medium 36 tok/s Pro
GPT-5 High 36 tok/s Pro
GPT-4o 106 tok/s Pro
Kimi K2 183 tok/s Pro
GPT OSS 120B 458 tok/s Pro
Claude Sonnet 4.5 37 tok/s Pro
2000 character limit reached

On the higher-order smallest ring star network of Chialvo neurons under diffusive couplings (2405.06000v1)

Published 9 May 2024 in nlin.AO and nlin.CD

Abstract: We put forward the dynamical study of a novel higher-order small network of Chialvo neurons arranged in a ring-star topology, with the neurons interacting via linear diffusive couplings. This model is perceived to imitate the nonlinear dynamical properties exhibited by a realistic nervous system where the neurons transfer information through higher-order multi-body interactions. We first analyze our model using the tools from nonlinear dynamics literature: fixed point analysis, Jacobian matrix, and bifurcation patterns. We observe the coexistence of chaotic attractors, and also an intriguing route to chaos starting from a fixed point, to period-doubling, to cyclic quasiperiodic closed invariant curves, to ultimately chaos. We numerically observe the existence of codimension-1 bifurcation patterns: saddle-node, period-doubling, and Neimark Sacker. We also qualitatively study the typical phase portraits of the system and numerically quantify chaos and complexity using the 0-1 test and sample entropy measure respectively. Finally, we study the collective behavior of the neurons in terms of two synchronization measures: the cross-correlation coefficient, and the Kuramoto order parameter.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (92)
  1. E.M. Izhikevich. Dynamical systems in neuroscience: The Geometry of Excitability and Bursting. MIT press, 2007.
  2. Neuronal dynamics: From single neurons to networks and models of cognition. Cambridge University Press, 2014.
  3. F. He and Y. Yang. Nonlinear system identification of neural systems from neurophysiological signals. Neuroscience, 458:213–228, 2021.
  4. R. FitzHugh. Impulses and physiological states in theoretical models of nerve membrane. Biophys. J., 1(6):445–466, 1961.
  5. A model of neuronal bursting using three coupled first order differential equations. Trans. R. Soc. B: Biol. Sci., 221(1222):87–102, 1984.
  6. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol., 117(4):500, 1952.
  7. Stability of synchronization in simplicial complexes. Nat. Commun., 12(1):1255, 2021.
  8. Dynamics on networks with higher-order interactions. Chaos, 33(4), 2023.
  9. First-order transition to oscillation death in coupled oscillators with higher-order interactions. Phys. Rev. E, 108:044207, Oct 2023.
  10. Networks beyond pairwise interactions: Structure and dynamics. Phys. Rep., 874:1–92, 2020. Networks beyond pairwise interactions: Structure and dynamics.
  11. Higher-order molecular organization as a source of biological function. Bioinformatics, 34(17):i944–i953, 2018.
  12. Higher-order interactions characterized in cortical activity. J. Neurosci., 31(48):17514–17526, 2011.
  13. On the presence of high-order interactions among somatosensory neurons and their effect on information transmission. J. Phys. Conf. Ser., 197:012013, 2009.
  14. Synchronization in hindmarsh–rose neurons subject to higher-order interactions. Chaos, 32(1), 2022.
  15. Synchronization of a higher-order network of rulkov maps. Chaos, 32(12), 2022.
  16. Impact of higher order network structure on emergent cortical activity. Netw. Neurosci., 4(1):292–314, 03 2020.
  17. High-order interdependencies in the aging brain. Brain Connect., 11(9):734–744, 2021.
  18. Genuine high-order interactions in brain networks and neurodegeneration. Neurobiol. Dis., 175:105918, 2022.
  19. Neurodegeneration: what is it and where are we? J. Clin. Invest., 111(1):3–10, 2003.
  20. Brain networks and epilepsy development in patients with Alzheimer disease. Brain Behav., 13(8):e3152, 2023.
  21. Between neurons and networks: investigating mesoscale brain connectivity in neurological and psychiatric disorders. Front. Neurosci., 18, February 2024.
  22. The physics of higher-order interactions in complex systems. Nat. Phys., 17(10):1093–1098, 2021.
  23. O. Omel’chenko and C.R. Laing. Collective states in a ring network of theta neurons. Proc. R. Soc. A, 478(2259):20210817, 2022.
  24. Chimera states in a ring of map-based neurons. Phys. A, 536(122596):122596, December 2019.
  25. F. Yang and J. Ma. Synchronization and energy balance of star network composed of photosensitive neurons. Eur. Phys. J. Spec. Top., 231(22):4025–4035, 2022.
  26. Multistability in a star network of Kuramoto-type oscillators with synaptic plasticity. Sci. Rep., 11(1):9840, 2021.
  27. S.S. Muni and A. Provata. Chimera states in ring–star network of Chua circuits. Nonlinear Dyn., 101(4):2509–2521, 2020.
  28. Dynamical effects of electromagnetic flux on chialvo neuron map: Nodal and network behaviors. Int. J. Bifurcat. Chaos, 32(09), 2022.
  29. On the analysis of a heterogeneous coupled network of memristive chialvo neurons. Nonlinear Dyn., 111:17499–17518, 2023.
  30. E. Van Vleck and B. Wang. Attractors for lattice Fitzhugh–Nagumo systems. Phys. D, 212(3-4):317–336, 2005.
  31. Noise-induced synchronization in a lattice Hodgkin–Huxley neural network. Phys. A, 393:638–645, 2014.
  32. L. Lei and J. Yang. Patterns in coupled Fitzhugh–Nagumo model on duplex networks. Chaos Solit. Fractals, 144:110692, 2021.
  33. Counterpart synchronization of duplex networks with delayed nodes and noise perturbation. J. Stat. Mech-Theory E., 2015(11):P11021, 2015.
  34. I. Daňo. Two Notes on Continuous-Time Neurodynamical Systems. Springer Berlin Heidelberg, 2012.
  35. Map-based models in neuronal dynamics. Phys. Rep., 501(1-2):1–74, April 2011.
  36. Refractoriness and neural precision. J. Neurosci., 18(6):2200–2211, 1998.
  37. D.R. Chialvo. Generic excitable dynamics on a two-dimensional map. Chaos Solit. Fractals, 5(3-4):461–479, 1995.
  38. Memristive Rulkov neuron model with magnetic induction effects. IEEE Trans. Industr. Inform., 18(3):1726–1736, 2022.
  39. R.A. Vazquez. Izhikevich neuron model and its application in pattern recognition. Aus. J. Intell. Inf. Process. Syst., 11(1):35–40, 2010.
  40. U. Feudel. Complex dynamics in multistable systems. Int. J. Bifurc. Chaos, 18(06):1607–1626, 2008.
  41. From the chaos to quasiregular patterns. In New Trends in Nonlinear Dynamics and Pattern-Forming Phenomena, pages 89–93. Springer US, New York, NY, 1990.
  42. G.A Gottwald and I. Melbourne. On the implementation of the 0–1 test for chaos. SIAM J. Appl. Dyn. Syst., 8(1):129–145, January 2009.
  43. G.A. Gottwald and I. Melbourne. The 0-1 test for chaos: A review. pages 221–247, 2016.
  44. A. Politi. Lyapunov exponent. Scholarpedia J., 8(3):2722, 2013.
  45. Physiological time-series analysis using approximate entropy and sample entropy. Am. J. Physiol. Heart Circ. Physiol., 278(6), 2000.
  46. C.E. Shannon. A mathematical theory of communication. ACM SIGMOBILE Mob. Comput. Commun. Rev., 5(1):3–55, January 2001.
  47. N.M Timme and C. Lapish. A tutorial for information theory in neuroscience. eNeuro, 5(3):ENEURO.0052–18.2018, May 2018.
  48. A primer on entropy in neuroscience. Neurosci. Biobehav. Rev., 146:105070, 2023.
  49. Transfer entropy–a model-free measure of effective connectivity for the neurosciences. J. Comput. Neurosci., 30(1):45–67, February 2011.
  50. S.M. Pincus. Approximate entropy as a measure of system complexity. Proc. Natl. Acad. Sci., 88(6):2297–2301, 1991.
  51. Sample entropy and surrogate data analysis for alzheimer’s disease. Math. Biosci. Eng, 16(6):6892–6906, 2019.
  52. Complex dynamics and phase synchronization in spatially extended ecological systems. Nature, 399(6734):354–359, May 1999.
  53. I.D. Couzin. Synchronization: The key to effective communication in animal collectives. Trends Cogn. Sci., 22(10):844–846, 2018. Special Issue: Time in the Brain.
  54. D.J.T. Sumpter. The principles of collective animal behaviour. Philos. Trans. R. Soc. Lond. B Biol. Sci., 361(1465):5–22, January 2006.
  55. S. Strogatz. Synchronization: A universal concept in nonlinear sciences. Phys. Today, 56(1):47–47, 01 2003.
  56. Synchronization of complex human networks. Nat. Commun., 11(1):3854, August 2020.
  57. Y. Kuramoto and D. Battogtokh. Coexistence of coherence and incoherence in nonlocally coupled phase oscillators. 2002.
  58. Asynchronous eye closure as an anti-predator behavior in the western fence lizard (sceloporus occidentalis). Ethology, 112:286 – 292, 12 2005.
  59. R. Sarfati and O. Peleg. Chimera states among synchronous fireflies. Sci. Adv., 8(46):eadd6690, November 2022.
  60. Self-organized alternating chimera states in oscillatory media. Sci. Rep., 5(1):9883, April 2015.
  61. Chimera states in mechanical oscillator networks. Proc. Natl. Acad. Sci. U. S. A., 110(26):10563–10567, June 2013.
  62. M. Wickramasinghe and I.Z. Kiss. Spatially organized dynamical states in chemical oscillator networks: synchronization, dynamical differentiation, and chimera patterns. PLoS One, 8(11):e80586, November 2013.
  63. Correlation analysis of the coherence-incoherence transition in a ring of nonlocally coupled logistic maps. Chaos, 26(9), 2016.
  64. Mechanism of solitary state appearance in an ensemble of nonlocally coupled Lozi maps. Eur. Phys. J. Spec. Top., 227(10):1173–1183, 2018.
  65. Y. Kuramoto. Chemical oscillations, waves, and turbulence, volume 8. Springer, 1984.
  66. S.H. Strogatz. From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Phys. D, 143(1-4):1–20, 2000.
  67. Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review. J. Math. Neurosci., 10(1):9, 2020.
  68. Repulsive inter-layer coupling induces anti-phase synchronization. Chaos, 31(6), 2021.
  69. Controlling chimera and solitary states by additive noise in networks of chaotic maps. J. Differ. Equ. Appl., 29(9-12):909–930, 2023.
  70. A. Provata. From Turing patterns to chimera states in the 2d brusselator model. Chaos, 33(3), 2023.
  71. K. Anesiadis and A. Provata. Synchronization in multiplex leaky integrate-and-fire networks with nonlocal interactions. Front. Netw. Physiol., 2:910862, 2022.
  72. Matcontm, a toolbox for continuation and bifurcation of cycles of maps: command line use. Department of Mathematics, Utrecht University, 2017.
  73. Numerical Bifurcation Analysis of Maps: From Theory to Software. Cambridge Monographs on Applied and Computational Mathematics. Cambridge University press, 2019.
  74. What are higher-order networks? SIAM Rev., 65(3):686–731, 2023.
  75. C. Berge. Hypergraphs: combinatorics of finite sets, volume 45. Elsevier, 1984.
  76. F. Wang and H. Cao. Mode locking and quasiperiodicity in a discrete-time chialvo neuron model. Commun. Nonlinear Sci. Numer. Simul., 56:481–489, 2018.
  77. P. Pilarczyk and G. Graff. An absorbing set for the chialvo map. Commun. Nonlinear Sci. Numer. Simul., page 107947, 2024.
  78. Initial-offset-boosted coexisting hyperchaos in a 2d memristive Chialvo neuron map and its application in image encryption. Nonlinear Dyn., 111(21):20447–20463, 2023.
  79. Noise-induced complex dynamics and synchronization in the map-based chialvo neuron model. Commun. Nonlinear Sci. Numer. Simul., 116:106867, 2023.
  80. S. Li. Network synchronization under periodic coupling of both positive and negative values. Eur. Phys. J. B, 96(6), 2023.
  81. Dynamics on higher-order networks: A review. J. R. Soc. Interface, 19(188):20220043, 2022.
  82. A week in the life of the human brain: stable states punctuated by chaotic transitions. Research Square, 2024.
  83. Toward a complex system understanding of bipolar disorder: a chaotic model of abnormal circadian activity rhythms in euthymic bipolar disorder. Aust. N.Z.J. Psychiatry, 50(8):783–792, 2016.
  84. A. Schnitzler and J. Gross. Normal and pathological oscillatory communication in the brain. Nat. Rev. Neurosci., 6(4):285–296, 2005.
  85. Modulation of long-range neural synchrony reflects temporal limitations of visual attention in humans. Proc. Natl. Acad. Sci. USA, 101(35):13050–13055, 2004.
  86. P. Brown. Oscillatory nature of human basal ganglia activity: relationship to the pathophysiology of Parkinson’s disease. Mov. Disord., 18(4):357–363, 2003.
  87. D.G. Margineanu. Epileptic hypersynchrony revisited. Neuroreport, 21(15):963–967, 2010.
  88. W.J.F. Govaerts. Numerical methods for bifurcations of dynamical equilibria. Society for Industrial and Applied Mathematics, USA, 2000.
  89. G.A. Gottwald and I. Melbourne. On the validity of the 0–1 test for chaos. Nonlinearity, 22(6):1367, 2009.
  90. amitg7/01chaostest.jl: 0-1 test for chaos - distinguish between regular and chaotic dynamics in deterministic dynamical systems. https://github.com/amitg7/01ChaosTest.jl.
  91. C. Schölzel. Nonlinear measures for dynamical systems, 2019.
  92. A simple guide to chaos and complexity. J. Epidemiol. Community Health., 61(11):933–937, 2007.

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Lightbulb Streamline Icon: https://streamlinehq.com

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets

This paper has been mentioned in 1 tweet and received 0 likes.

Upgrade to Pro to view all of the tweets about this paper:

Start a free 7-day Pro trial