title: Achieving modulated oscillations by feedback control.
abstract: In this paper, we develop an approach to achieve either frequency or amplitude modulation of an oscillator merely through feedback control. We present and implement a unified theory of our approach for any finite-dimensional continuous dynamical system that exhibits oscillatory behavior. The approach is illustrated not only for the normal forms of dynamical systems but also for representative biological models, such as the isolated and coupled FitzHugh-Nagumo model. We demonstrate the potential usefulness of our approach to uncover the mechanisms of frequency and amplitude modulations experimentally observed in a wide range of real systems.
authors.affiliation: School of Mathematical Sciences, Centre for Computational Systems Biology, Fudan University, Shanghai 200433, China, and Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Education, China and Department of Computer Science, University of Warwick, Coventry CV4 7AL, United Kingdom.
authors.forename: Tian
authors.initials: T
authors.lastname: Ge
authors.affiliation: School of Mathematical Sciences, Centre for Computational Systems Biology, Fudan University, Shanghai 200433, China, and Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Education, China.
authors.forename: Xiaoying
authors.initials: X
authors.lastname: Tian
authors.affiliation: Potsdam Institute for Climate Impact Research, D-14412 Potsdam, Germany and Department of Physics, Humboldt University of Berlin, D-12489 Berlin, Germany and Department of Control Theory, Nizhny Novgorod State University, Gagarin Avenue 23, 606950 Nizhny Novgorod, Russia.
authors.forename: Jürgen
authors.initials: J
authors.lastname: Kurths
authors.affiliation: School of Mathematical Sciences, Centre for Computational Systems Biology, Fudan University, Shanghai 200433, China, and Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Education, China and Department of Computer Science, University of Warwick, Coventry CV4 7AL, United Kingdom.
authors.forename: Jianfeng
authors.initials: J
authors.lastname: Feng
authors.affiliation: School of Mathematical Sciences, Centre for Computational Systems Biology, Fudan University, Shanghai 200433, China, and Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Education, China.
authors.forename: Wei
authors.initials: W
authors.lastname: Lin
mesh_terms: D005246:Feedback; D008564:Membrane Potentials / Q000502:physiology; D008962:Models, Theoretical; D009474:Neurons / Q000502:physiology; D010507:Periodicity