Abstract
In this chapter, we extend the master stability approach to complex dynamical networks of diffusively and adaptively coupled oscillators. We show how the interplay between adaptivity and network structure gives rise to the formation of stability islands. Moreover, we report a desynchronization transition and the emergence of complex partial synchronization patterns induced by an increasing overall coupling strength. We illustrate our findings using adaptive networks of coupled phase oscillators.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Pecora LM, Carroll TL (1998) Master stability functions for synchronized coupled systems. Phys Rev Lett 80:2109
Keane A, Dahms T, Lehnert J, Suryanarayana SA, Hövel P, Schöll E (2012) Synchronisation in networks of delay-coupled type-I excitable systems. Eur Phys J B 85:407
Lehnert J (2016) Controlling synchronization patterns in complex networks, Springer Theses. Springer, Heidelberg
Berner R, Vock S, Schöll E, Yanchuk S (2021) Desynchronization transitions in adaptive networks. Phys Rev Lett 126:028301
Vock S, Berner R, Yanchuk S, Schöll E (2021) Effect of diluted connectivities on cluster synchronization of adaptively coupled oscillator networks. arXiv:2101.05601
Kasatkin DV, Yanchuk S, Schöll E, Nekorkin VI (2017) Self-organized emergence of multi-layer structure and chimera states in dynamical networks with adaptive couplings. Phys Rev E 96
Kasatkin DV, Nekorkin VI (2018) Synchronization of chimera states in a multiplex system of phase oscillators with adaptive couplings. Chaos 28
Kasatkin DV, Nekorkin VI (2018) The effect of topology on organization of synchronous behavior in dynamical networks with adaptive couplings. Eur Phys J Spec Top 227:1051
Dahms T, Lehnert J, Schöll E (2012) Cluster and group synchronization in delay-coupled networks. Phys Rev E 86
Pecora LM, Sorrentino F, Hagerstrom AM, Murphy TE, Roy R (2014) Symmetries, cluster synchronization, and isolated desynchronization in complex networks. Nat Commun 5:4079
Sorrentino F, Pecora LM, Hagerstrom AM, Murphy TE, Roy R (2016) Complete characterization of the stability of cluster synchronization in complex dynamical networks. Sci Adv 2
Sorrentino F, Ott E (2007) Network synchronization of groups. Phys Rev E 76
Flunkert V, Yanchuk S, Dahms T, Schöll E (2010) Synchronizing distant nodes: a universal classification of networks. Phys Rev Lett 105
Dahms T (2011) Synchronization in delay-coupled laser networks. Ph.D. thesis, Technische Universität Berlin
Heiligenthal S, Dahms T, Yanchuk S, Jüngling T, Flunkert V, Kanter I, Schöll E, Kinzel W (2011) Strong and weak chaos in nonlinear networks with time-delayed couplings. Phys Rev Lett 107
Kyrychko YN, Blyuss KB, Schöll E (2014) Synchronization of networks of oscillators with distributed-delay coupling. Chaos 24
Wille C, Lehnert J, Schöll E (2014) Synchronization-desynchronization transitions in complex networks: an interplay of distributed time delay and inhibitory nodes. Phys Rev E 90
Ladenbauer J, Lehnert J, Rankoohi H, Dahms T, Schöll E, Obermayer K (2013) Adaptation controls synchrony and cluster states of coupled threshold-model neurons. Phys Rev E 88
Coombes S, Thul R (2016) Synchrony in networks of coupled non-smooth dynamical systems: extending the master stability function. Eur J Appl Math 27:904
Stilwell DJ, Bollt EM, Roberson DG (2006) Sufficient conditions for fast switching synchronization in time-varying network topologies. SIAM J Appl Dyn Syst 5:140
Kohar V, Ji P, Choudhary A, Sinha S, Kurths J (2014) Synchronization in time-varying networks. Phys Rev E 90
Zhou C, Kurths J (2006) Dynamical weights and enhanced synchronization in adaptive complex networks. Phys Rev Lett 96
Sorrentino F, Ott E (2008) Adaptive synchronization of dynamics on evolving complex networks. Phys Rev Lett 100
Belykh VN, Belykh IV, Hasler M (2004) Connection graph stability method for synchronized coupled chaotic systems. Phys D 195:159
Belykh IV, Belykh VN, Hasler M (2004) Blinking model and synchronization in small-world networks with a time-varying coupling. Phys D 195:188
Belykh IV, de Lange E, Hasler M (2005) Synchronization of bursting neurons: what matters in the network topology. Phys Rev Lett 94
Belykh IV, Belykh VN, Hasler M (2006) Generalized connection graph method for synchronization in asymmetrical networks. Phys D 224:42
Belykh IV, Belykh VN, Hasler M (2006) Synchronization in asymmetrically coupled networks with node balance. Chaos 16
Daley K, Zhao K, Belykh IV (2020) Synchronizability of directed networks: the power of non-existent ties. Chaos 30
Yu W, DeLellis P, Chen G, di Bernardo M, Kurths J (2012) Distributed adaptive control of synchronization in complex networks. IEEE Trans Autom Control 57:2153
De Lellis P, di Bernardo M, Garofalo F, Porfiri M (2010) Evolution of complex networks via edge snapping. IEEE Trans Circuits Syst I 57:2132
Lehnert J, Hövel P, Selivanov AA, Fradkov AL, Schöll E (2014) Controlling cluster synchronization by adapting the topology. Phys Rev E 90
Hövel P, Lehnert J, Selivanov A, Fradkov AL, Schöll E (2016) Adaptively controlled synchronization of delay-coupled networks. In: Schöll E, Klapp SHL, Hövel P (eds) Control of self-organizing nonlinear systems. Springer, Berlin, pp 47–63
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Berner, R. (2021). Synchronization on Adaptive Complex Network Structures. In: Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-74938-5_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-74938-5_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-74937-8
Online ISBN: 978-3-030-74938-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)