Complexity and irreducibility of dynamics on networks of networks

Abstract

We study numerically the dynamics of a network of all-to-all-coupled, identical sub-networks consisting of diffusively coupled, non-identical FitzHugh--Nagumo oscillators. For a large range of within- and between-network couplings, the network exhibits a variety of dynamical behaviors, previously described for single, uncoupled networks. We identify a region in parameter space in which the interplay of within- and between-network couplings allows for a richer dynamical behavior than can be observed for a single sub-network. Adjoining this atypical region, our network of networks exhibits transitions to multistability. We elucidate bifurcations governing the transitions between the various dynamics when crossing this region and discuss how varying the couplings affects the effective structure of our network of networks. Our findings indicate that reducing a network of networks to a single (but bigger) network might be not accurate enough to properly understand the complexity of its dynamics.

arXiv comment8 figures

References in corpus (38)

• Epidemic processes in complex networks
• Synchronization in complex networks
• Multilayer Networks
• The structure and dynamics of multilayer networks
• Spatial Networks
• Interdependent networks: Reducing the coupling strength leads to a change from a first to second order percolation transition
• Robustness of a Network of Networks
• The physics of spreading processes in multilayer networks
• Layer aggregation and reducibility of multilayer interconnected networks
• Complex networks in climate dynamics - Comparing linear and nonlinear network construction methods
• The Multilayer Nature of Ecological Networks
• Centrality in Interconnected Multilayer Networks
• Explosive synchronization in adaptive and multilayer networks
• Layered Complex Networks
• Networks in Cognitive Science
• Partially integrable dynamics of hierarchical populations of coupled oscillators
• Synchronization of two interacting populations of oscillators
• Synchronization in networks with multiple interaction layers
• Mapping multiplex hubs in human functional brain network
• Hidden geometric correlations in real multiplex networks
• Synchronization in networks of networks: the onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators
• Redundant interdependencies boost the robustness of multilayer networks
• Evolving networks in the human epileptic brain
• Extreme events in excitable systems and mechanisms of their generation
• Inter-layer synchronization in multiplex networks
• Optimal percolation on multiplex networks
• Multiple Tipping Points and Optimal Repairing in Interacting Networks
• Route to extreme events in excitable systems
• Irreducibility of multilayer network dynamics: the case of the voter model
• Breathing synchronization in interconnected networks
• Efficiently and easily integrating differential equations with JiTCODE, JiTCDDE, and JiTCSDE
• Collective oscillations in disordered neural networks
• The interdependent network of gene regulation and metabolism is robust where it needs to be
• Self-induced switchings between multiple space-time patterns on complex networks of excitable units
• Asymmetry-Induced Synchronization in Oscillator Networks
• Collective dynamics in two populations of noisy oscillators with asymmetric interactions
• Coupled networks and networks with bimodal frequency distributions are equivalent
• Interplay of Delay and multiplexing: Impact on Cluster Synchronization