title: Restoration of rhythmicity in diffusively coupled dynamical networks.
abstract: Oscillatory behaviour is essential for proper functioning of various physical and biological processes. However, diffusive coupling is capable of suppressing intrinsic oscillations due to the manifestation of the phenomena of amplitude and oscillation deaths. Here we present a scheme to revoke these quenching states in diffusively coupled dynamical networks, and demonstrate the approach in experiments with an oscillatory chemical reaction. By introducing a simple feedback factor in the diffusive coupling, we show that the stable (in)homogeneous steady states can be effectively destabilized to restore dynamic behaviours of coupled systems. Even a feeble deviation from the normal diffusive coupling drastically shrinks the death regions in the parameter space. The generality of our method is corroborated in diverse non-linear systems of diffusively coupled paradigmatic models with various death scenarios. Our study provides a general framework to strengthen the robustness of dynamic activity in diffusively coupled dynamical networks.
authors.affiliation: School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China.|Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China.|Potsdam Institute for Climate Impact Research, Telegraphenberg, D-14415 Potsdam, Germany.
authors.forename: Wei
authors.initials: W
authors.lastname: Zou
authors.affiliation: Potsdam Institute for Climate Impact Research, Telegraphenberg, D-14415 Potsdam, Germany.|Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA University, Thanjavur 613401, India.
authors.forename: D V
authors.initials: DV
authors.lastname: Senthilkumar
authors.affiliation: Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St Louis, Missouri 63103, USA.
authors.forename: Raphael
authors.initials: R
authors.lastname: Nagao
authors.affiliation: Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St Louis, Missouri 63103, USA.
authors.forename: István Z
authors.initials: IZ
authors.lastname: Kiss
authors.affiliation: Potsdam Institute for Climate Impact Research, Telegraphenberg, D-14415 Potsdam, Germany.|The Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China.
authors.forename: Yang
authors.initials: Y
authors.lastname: Tang
authors.affiliation: Department of Systemic Cell Biology, Max Planck Institute of Molecular Physiology, Dortmund D-44227, Germany.|Research Centre for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Skopje, Macedonia.
authors.forename: Aneta
authors.initials: A
authors.lastname: Koseska
authors.affiliation: School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China.|Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China.|Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616, USA.
authors.forename: Jinqiao
authors.initials: J
authors.lastname: Duan
authors.affiliation: Potsdam Institute for Climate Impact Research, Telegraphenberg, D-14415 Potsdam, Germany.|Institute of Physics, Humboldt University Berlin, D-12489 Berlin, Germany.|Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3FX, UK.|Department of Control Theory, Nizhny Novgorod State University, Gagarin Avenue 23, 606950 Nizhny Novgorod, Russia.
authors.forename: Jürgen
authors.initials: J
authors.lastname: Kurths
mesh_terms: D003198:Computer Simulation; D008962:Models, Theoretical; D010507:Periodicity; D013597:Systems Analysis