title: Chaotic, informational and synchronous behaviour of multiplex networks.
abstract: The understanding of the relationship between topology and behaviour in interconnected networks would allow to charac- terise and predict behaviour in many real complex networks since both are usually not simultaneously known. Most previous studies have focused on the relationship between topology and synchronisation. In this work, we provide analytical formulas that shows how topology drives complex behaviour: chaos, information, and weak or strong synchronisation; in multiplex net- works with constant Jacobian. We also study this relationship numerically in multiplex networks of Hindmarsh-Rose neurons. Whereas behaviour in the analytically tractable network is a direct but not trivial consequence of the spectra of eigenvalues of the Laplacian matrix, where behaviour may strongly depend on the break of symmetry in the topology of interconnections, in Hindmarsh-Rose neural networks the nonlinear nature of the chemical synapses breaks the elegant mathematical connec- tion between the spectra of eigenvalues of the Laplacian matrix and the behaviour of the network, creating networks whose behaviour strongly depends on the nature (chemical or electrical) of the inter synapses.
authors.affiliation: Institute for Complex Systems and Mathematical Biology, SUPA, University of Aberdeen, Aberdeen, United Kingdom.
authors.forename: M S
authors.initials: MS
authors.lastname: Baptista
authors.affiliation: Department of Physics, Federal University of Technology - Paraná, 84016-210, Ponta Grossa, Paraná, Brazil.
authors.forename: R M
authors.initials: RM
authors.lastname: Szmoski
authors.affiliation: Department of Mathematics, Federal University of Technology - Paraná, 84016-210, Ponta Grossa, Paraná, Brazil.
authors.forename: R F
authors.initials: RF
authors.lastname: Pereira
authors.affiliation: Departamento de Física, Universidade Estadual de Ponta Grossa, 84030-900, Paraná, Brazil.
authors.forename: S E de Souza
authors.initials: SE
authors.lastname: Pinto