One- and two-cluster synchronized dynamics of non-diffusively coupled Tchebycheff map networks |
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| Authors: | Mirko Schäfer Martin Greiner |
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| Institution: | 1. Aarhus School of Engineering and Department of Mathematical Sciences, Aarhus University, Aarhus, Denmark;2. Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe University, Frankfurt, Germany;1. Department of Engineering, Aarhus University, Inge Lehmanns Gade 10, 8000 Aarhus, Denmark;2. iCLIMATE Interdisciplinary Centre for Climate Change, Aarhus University, Denmark;3. Institute for Automation and Applied Informatics (IAI), Karlsruhe Institute of Technology (KIT), Forschungszentrum 449, 76344 Eggenstein-Leopoldshafen, Germany;1. Institute for Automation and Applied Informatics, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany;2. Frankfurt Institute for Advanced Studies, Ruth-Moufang-Straße 1, 60438 Frankfurt am Main, Germany;3. Department of Engineering, Aarhus University, 8000 Aarhus C, Denmark;1. Frankfurt Institute for Advanced Studies, 60438 Frankfurt am Main, Germany;2. Department of Engineering, Aarhus University, 8000 Aarhus C, Denmark;3. Department of Electrical Engineering and Computer Science, Kassel University, 34125 Kassel, Germany;4. Fraunhofer IWES, 34119 Kassel, Germany;1. Center for Mathematical Sciences, Technische Universität München, Boltzmannstraße 3, 85748 Garching, Germany;2. Department of Engineering, Aarhus University, Ny Munkegade 118, 8000 Aarhus C, Denmark;3. Department of Mathematics, Aarhus University, Ny Munkegade 118, 8000 Aarhus C, Denmark;1. Department of Engineering, Aarhus University, 8000 Aarhus C, Denmark;2. Institute for Automation and Applied Informatics (IAI), Karlsruhe Institute of Technology (KIT), Forschungszentrum 449, 76344, Eggenstein-Leopoldshafen, Germany;1. Frankfurt Institute for Advanced Studies, Goethe-Universität, 60438 Frankfurt am Main, Germany;2. Department of Civil and Environmental Engineering, Stanford University, Stanford, CA, USA;3. Department of Physics, Aarhus University, 8000 Aarhus C, Denmark;4. Department of Engineering, Aarhus University, 8200 Aarhus N, Denmark;5. Department of Mathematics, Aarhus University, 8000 Aarhus C, Denmark |
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| Abstract: | We use the master stability formalism to discuss one- and two-cluster synchronization of coupled Tchebycheff map networks. For diffusively coupled map systems, the one-cluster synchronized dynamics is given by the behaviour of the individual maps, and the coupling only determines the stability of the coherent state. For the case of non-diffusive coupling and for two-cluster synchronization, the synchronized dynamics on networks is different from the behaviour of the single individual map. Depending on the coupling, we study numerically the characteristics of various forms of the resulting synchronized dynamics. The stability properties of the respective one-cluster synchronized states are discussed for arbitrary network structures. For the case of two-cluster synchronization on bipartite networks we also present analytical expressions for fixed points and zig-zag patterns, and explicitly determine the linear stability of these orbits for the special case of ring-networks. |
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