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Proceedings: Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, 3/2010, Volume 466, Issue 2115, pp. 771 - 788
Recent studies on stochastic oscillations mostly focus on the power spectral analysis. However, the power spectrum yields information only on the frequency of... 
Molecules | Determinism | Maps | Odes | Oscillation | Steady states | Ordinary differential equations | Limit cycles | Biochemistry | Kinetics | Cycle flux | Stochastic limit cycle | Poincaré map | cycle flux | CIRCULATION | LANDSCAPE | MULTIDISCIPLINARY SCIENCES | NETWORKS | NOISE | SYNCHRONIZED DYNAMICS | RESONANCE | CHEMICAL-SYSTEMS | KINETICS | oscillation | stochastic limit cycle | Poincare map
Journal Article
SIAM Journal on Applied Dynamical Systems, ISSN 1536-0040, 2018, Volume 17, Issue 3, pp. 2205 - 2233
We introduce a variational method for analyzing limit cycle oscillators in R-d driven by Gaussian noise. This allows us to derive exact stochastic differential... 
Phase reduction | Limit cycle | Stochastic oscillator | DENSITY | MATHEMATICS, APPLIED | limit cycle | ORNSTEIN-UHLENBECK PROCESS | DYNAMICS | NOISE | PHYSICS, MATHEMATICAL | phase reduction | stochastic oscillator
Journal Article
Physical Review Letters, ISSN 0031-9007, 11/2004, Volume 93, Issue 20, pp. 1 - 204103
We show that a wide class of uncoupled limit-cycle oscillators can be in-phase synchronized by common weak additive noise. An expression of the Lyapunov... 
INTERMITTENCY | NEOCORTICAL NEURONS | RESPONSES | PHYSICS, MULTIDISCIPLINARY | DYNAMICS | SYSTEMS | RELIABILITY | COUPLED OSCILLATORS | TRANSITIONS | STOCHASTIC RESONANCE | ARRAYS | Models, Theoretical | Models, Neurological | Neurons - physiology | Periodicity
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 01/2018, Volume 264, Issue 2, pp. 1019 - 1049
We study the effect of additive Brownian noise on an ODE system that has a stable hyperbolic limit cycle, for initial data that are attracted to the limit... 
Isochrons | Stochastic differential equations | Small noise limit | Stable hyperbolic limit cycles | Long time dynamics | MATHEMATICS | MOTION | INTERFACE | FLUCTUATIONS | GINZBURG-LANDAU EQUATION | DYNAMICS | Noise control | Analysis
Journal Article
Physical Review Letters, ISSN 0031-9007, 05/2009, Volume 102, Issue 19, p. 194102
We formulate a phase-reduction method for a general class of noisy limit cycle oscillators and find that the phase equation is parametrized by the ratio... 
PHYSICS, MULTIDISCIPLINARY | SYNCHRONIZATION | Models, Theoretical | Stochastic Processes | Noise | Physics - Adaptation and Self-Organizing Systems
Journal Article
Physical Review Letters, ISSN 0031-9007, 03/2014, Volume 112, Issue 11, p. 114101
The effects of noise on the dynamics of nonlinear systems is known to lead to many counterintuitive behaviors. Using simple planar limit cycle oscillators, we... 
SYSTEMS | DEATH | PHYSICS, MULTIDISCIPLINARY | STOCHASTIC RESONANCE | Models, Theoretical | Biological Clocks | Stochastic Processes | Rotation | Periodicity
Journal Article
The European Physical Journal B, ISSN 1434-6028, 6/2018, Volume 91, Issue 6, pp. 1 - 8
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 06/2017, Volume 127, Issue 6, pp. 1897 - 1925
Cyclic structure and dynamics are of great interest in both the fields of stochastic processes and nonequilibrium statistical physics. In this paper, we find a... 
Cycle flux | Excursion theory | Bessel process | Haldane equality | Nonequilibrium | STOCHASTIC DYNAMICS | ENTROPY PRODUCTION | FREE-ENERGY DIFFERENCES | EQUALITY | STATISTICS & PROBABILITY | MARKOV | Stochastic processes | Mathematics - Probability
Journal Article
IEEE Transactions on Automatic Control, ISSN 0018-9286, 12/2000, Volume 45, Issue 12, pp. 2432 - 2436
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 07/2011, Volume 84, Issue 1, p. 016229
We consider optimization of phase response curves for stochastic synchronization of noninteracting limit-cycle oscillators by common Poisson impulsive signals.... 
PHYSICS, FLUIDS & PLASMAS | SOMATOSENSORY CORTEX | DYNAMICS | POPULATIONS | SYSTEMS | RELIABILITY | PHYSICS, MATHEMATICAL | Linear Models | Poisson Distribution | Stochastic Processes | Normal Distribution | Physics - Adaptation and Self-Organizing Systems
Journal Article
Physical Review Letters, ISSN 0031-9007, 02/2004, Volume 92, Issue 7, pp. 739011 - 739014
We demonstrate experimentally and theoretically the existence of canard orbits and excitable quasiharmonic limit cycles in the thermo-optical dynamics of... 
SEMICONDUCTOR-LASERS | SYSTEM | WAVES | OPTICAL FEEDBACK | PHYSICS, MULTIDISCIPLINARY | ETALON | COHERENCE RESONANCE | NOISE | STOCHASTIC RESONANCE | Models, Theoretical | Biological Clocks | Semiconductors | Optics and Photonics | Models, Biological
Journal Article
Chaos: An Interdisciplinary Journal of Nonlinear Science, ISSN 1054-1500, 06/2012, Volume 22, Issue 2, p. 023140
Landscape is one of the key notions in literature on biological processes and physics of complex systems with both deterministic and stochastic dynamics. The... 
MATHEMATICS, APPLIED | STOCHASTIC DYNAMICS | CHEMICAL-REACTION | THERMODYNAMICS | MARKOV-CHAINS | FLUCTUATIONS | CHARACTERISTIC BOUNDARIES | SYSTEMS | DIFFUSION | MODEL | PHYSICS, MATHEMATICAL | METASTABILITY | Diffusion | Nonlinear Dynamics | Models, Biological
Journal Article
Chaos: An Interdisciplinary Journal of Nonlinear Science, ISSN 1054-1500, 09/2010, Volume 20, Issue 3, p. 033126
An effective white-noise Langevin equation is derived that describes long-time phase dynamics of a limit-cycle oscillator driven by weak stationary colored... 
oscillators | MATHEMATICS, APPLIED | diffusion | chaos | INPUT | random noise | COUPLED NEURAL OSCILLATORS | POPULATIONS | RELIABILITY | PHYSICS, MATHEMATICAL | nonlinear dynamical systems | NEURONS | SYSTEMS | INDUCED SYNCHRONIZATION | stochastic processes | STOCHASTIC RESONANCE | RESETTING CURVES | limit cycles | ACTIVE ROTATOR | Physics - Chaotic Dynamics
Journal Article
by ZHU, X.-M and YIN, L and AO, P
International Journal of Modern Physics B, ISSN 0217-9792, 03/2006, Volume 20, Issue 7, pp. 817 - 827
We demonstrate here that the potential can coexist with limit cycle in nonlinear dissipative dynamics, where the potential plays the driving role for dynamics... 
Dissipative and conservative dynamics | Limit cycle | Stochastic processes in nonequilibrium physics | PHYSICS, CONDENSED MATTER | limit cycle | PHYSICS, APPLIED | stochastic processes in nonequilibrium physics | PHYSICS, MATHEMATICAL | dissipative and conservative dynamics
Journal Article
Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, 2004, Volume 69, Issue 5, p. 8
Bistability generated via a pure noise-induced phase transition is reexamined from the view of bifurcations in macroscopic cumulant dynamics. It allows an... 
MULTIPLICATIVE NOISE | COLORED-NOISE | OSCILLATORS | PHYSICS, FLUIDS & PLASMAS | ADDITIVE NOISE | PHYSICS, MATHEMATICAL | STOCHASTIC RESONANCE | SPATIAL-PATTERNS
Journal Article
ROBOMECH Journal, ISSN 2197-4225, 12/2018, Volume 5, Issue 1, pp. 1 - 17
This paper addresses a reference gait speed generator for limit-cycle-based bipedal gait of humanoid robots in order to achieve secure and efficient... 
Engineering | Mechatronics | Control | Computational Intelligence | 3-D bipedal gait | Artificial Intelligence (incl. Robotics) | Artificial potential field | Leader-follower control | Stochastic optimization | Robotics and Automation
Journal Article
Chaos: An Interdisciplinary Journal of Nonlinear Science, ISSN 1054-1500, 03/2008, Volume 18, Issue 1, p. 015111
A detailed asymptotic study of the effect of small Gaussian white noise on a relaxation oscillator undergoing a supercritical Hopf bifurcation is presented.... 
MATHEMATICS, APPLIED | SINGULAR HOPF-BIFURCATION | DYNAMICS | SYSTEMS | MECHANISMS | PHYSICS, MATHEMATICAL | STOCHASTIC RESONANCE | Algorithms | Biological Clocks - physiology | Models, Biological | Computer Simulation | Feedback - physiology | Models, Statistical | Nonlinear Dynamics
Journal Article
Algorithms, ISSN 1999-4893, 11/2018, Volume 11, Issue 11, p. 169
This work addresses parameter estimation of a class of neural systems with limit cycles. An identification model is formulated based on the discretized neural... 
Innovation | Parameter estimation | Stochastic gradient algorithm | Recursive least-squares algorithm | Neural system | innovation | parameter estimation | neural system | recursive least-squares algorithm | stochastic gradient algorithm
Journal Article
Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, 09/2008, Volume 2008, Issue 9, p. P09001
Fluctuations and noise may alter the behaviour of dynamical systems considerably. For example, oscillations may be sustained by demographic fluctuations in... 
Dynamical processes (theory) | Nonlinear dynamics | Fluctuations (theory) | Stochastic processes (theory) | SIZE | BRUSSELATOR | MODEL | PHYSICS, MATHEMATICAL | CLOCKS | dynamical processes (theory) | fluctuations (theory) | MECHANICS | stochastic processes (theory) | FLUCTUATIONS | EPIDEMICS | OSCILLATIONS | nonlinear dynamics | BIFURCATION
Journal Article