Coupled nonlinear oscillators and the symmetries of animal gaits
From MaRDI portal
Publication:1313238
DOI10.1007/BF02429870zbMath0808.92012WikidataQ56227204 ScholiaQ56227204MaRDI QIDQ1313238
Publication date: 26 January 1994
Published in: Journal of Nonlinear Science (Search for Journal in Brave)
coupled nonlinear oscillatorsoscillator networkslocomotioncentral pattern generatorsneural circuitsobserved symmetries of gaitsperiodic patterns of leg movementssymmetry- breaking bifurcationssymmetry-breaking oscillation patterns
Related Items (80)
Robust phase-waves in chains of half-center oscillators ⋮ Mathematical frameworks for oscillatory network dynamics in neuroscience ⋮ Quasi-pinning synchronization and stabilization of fractional order BAM neural networks with delays and discontinuous neuron activations ⋮ Dynamics of two-cell systems with discrete delays ⋮ A group-theoretic approach to rings of coupled biological oscillators ⋮ In-phase and antiphase self-oscillations in a model of two electrically coupled pacemakers ⋮ Hard-wired central pattern generators for quadrupedal locomotion ⋮ SYNCHRONOUS/ASYNCHRONOUS PATTERNS IN THREE-CELL NETWORKS WITH MULTIPLE TIME DELAYS ⋮ The Influence of Limit Cycle Topology on the Phase Resetting Curve ⋮ Beyond in-phase and anti-phase coordination in a model of joint action ⋮ Survey of locomotion control of legged robots inspired by biological concept ⋮ Reconstruction of the spatio-temporal dynamics of a human magnetoencephalogram ⋮ An adaptive feedback control for chaos synchronization of nonlinear systems with different order ⋮ Symmetry-breaking in a rate model for a biped locomotion central pattern generator ⋮ Dynamical symmetries and temporal segmentation ⋮ New exponential synchronization criteria for time-varying delayed neural networks with discontinuous activations ⋮ Global pulse synchronization of chaotic oscillators through fast-switching: theory and experiments ⋮ Inhomogeneous stationary and oscillatory regimes in coupled chaotic oscillators ⋮ COHERENT SYNCHRONIZATION IN LINEARLY COUPLED NONLINEAR SYSTEMS ⋮ Fractional central pattern generators for bipedal locomotion ⋮ Oscillator death in coupled biochemical oscillators ⋮ Synchronization in light-controlled oscillators ⋮ Weak synchronization of chaotic neural networks with parameter mismatch via periodically intermittent control ⋮ Analysis of bifurcation in a system of \(n\) coupled oscillators with delays ⋮ Noninvasive Stabilization of Periodic Orbits in O4-Symmetrically Coupled Systems Near a Hopf Bifurcation Point ⋮ Stable Synchronous Propagation of Signals by Feedforward Networks ⋮ New conditions on synchronization of networks of linearly coupled dynamical systems with non-Lipschitz right-hand sides ⋮ Phase-flip in relay oscillators via linear augmentation ⋮ Application of mode decomposition approach to the synchronization of the non-identical dynamical systems ⋮ The Effects of Delay on the HKB Model of Human Motor Coordination ⋮ Hölder exponent spectra for human gait ⋮ Central pattern generators for bipedal locomotion ⋮ Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review ⋮ Rigid patterns of synchrony for equilibria and periodic cycles in network dynamics ⋮ Bistability of patterns of synchrony in Kuramoto oscillators with inertia ⋮ Gait Transitions in a Phase Oscillator Model of an Insect Central Pattern Generator ⋮ Stability and bifurcation analysis of delay coupled Van der Pol-Duffing oscillators ⋮ Numerical detection of patterns in CPGs: gait patterns in insect movement ⋮ Stability of echo waves in linearly coupled oregonators ⋮ Stability analysis and robust synchronization of fractional‐order competitive neural networks with different time scales and impulsive perturbations ⋮ A modular network for legged locomotion. ⋮ A general family of morphed nonlinear phase oscillators with arbitrary limit cycle shape ⋮ Modelling gait transition in two-legged animals ⋮ Synchronization of a class of strictly different chaotic oscillators ⋮ Concepts of synchronization in dynamical systems ⋮ Local attractors, degeneracy and analyticity: symmetry effects on the locally coupled Kuramoto model ⋮ Synchronization and stability for quantum Kuramoto ⋮ Oscillation analysis of linearly coupled piecewise affine systems: application to spatio-temporal neuron dynamics ⋮ Dynamics of Oscillatory Networks with Pulse Delayed Coupling ⋮ Symmetry methods in mathematical biology ⋮ The Haken-Kelso-Bunz (HKB) model: from matter to movement to mind ⋮ Two dimensionless parameters and a mechanical analogue for the HKB model of motor coordination ⋮ Contraction principle and its applications in synchronization of nonlinearly coupled systems ⋮ Interior symmetry and local bifurcation in coupled cell networks ⋮ Mode decomposition for a synchronous state and its applications ⋮ Weak and non-resonant double Hopf bifurcations in \(m\) coupled van der Pol oscillators with delay coupling ⋮ Synchronization between interacting ensembles of globally coupled chaotic maps ⋮ Dynamical behavior in linearly coupled Oregonators. ⋮ Bifurcations and synchronization in networks of unstable reaction-diffusion systems ⋮ On partial contraction analysis for coupled nonlinear oscillators ⋮ Overdetermined constraints and rigid synchrony patterns for network equilibria ⋮ Master-slave synchronization of continuously and intermittently coupled sampled-data chaotic oscillators ⋮ Dynamic properties of VDP-CPG model in rhythmic movement with delay ⋮ Hexapodal gaits and coupled nonlinear oscillator models ⋮ Modulation of synchronization dynamics in a network of self-sustained systems ⋮ Symmetry and phase-locking in a ring of pulse-coupled oscillators with distributed delays ⋮ A dynamical model for mirror movements ⋮ Spatiotemporal dynamics in a ring of N mutually coupled self-sustained systems ⋮ Nonlinear dynamics of networks: the groupoid formalism ⋮ Characterization and Computation of Partial Synchronization Manifolds for Diffusive Delay-Coupled Systems ⋮ Clustering in neural networks with heterogeneous and asymmetrical coupling strengths ⋮ A framework for synchronization theory ⋮ The synchronized dynamics of time-varying networks ⋮ EXOTIC DYNAMICS IN NETWORKS OF COUPLED RINGS OF CELLS ⋮ Phase-locking modes in a bidimensional network of coupled water jets ⋮ Dynamics of a limit cycle oscillator under time delayed linear and nonlinear feedbacks ⋮ Heteroclinic cycles in rings of coupled cells ⋮ Dynamics of multifrequency coordination using parametric driving: theory and experiment ⋮ Spontaneous Symmetry-Breaking in a Network Model for Quadruped Locomotion ⋮ Forced nonlinear resonance in a system of coupled oscillators
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Bifurcation and symmetry breaking
- Three coupled oscillators: Mode-locking, global bifurcations and toroidal chaos
- Coordination of many oscillators and generation of locomotory patterns
- The behavior of rings of coupled oscillators
- The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: a mathematical model
- Symmetry-breaking bifurcation: A possible mechanism for 2:1 frequency- locking in animal locomotion
- Singularities and groups in bifurcation theory. Volume II
- Mutually synchronized relaxation oscillators as prototypes of oscillating systems in biology
- The dynamics of \(n\) weakly coupled identical oscillators
- Hexapodal gaits and coupled nonlinear oscillator models
- Some finite state aspects of legged locomotion
- Some properties of regularly realizable gait matrices
- Three identical oscillators with symmetric coupling
- Symmetric chaos in systems of three and four forced oscillators
- Patterns at Primary Hopf Bifurcations of a Plexus of Identical Oscillators
- Hopf bifurcation with the symmetry of the square
- Symmetric patterns in linear arrays of coupled cells
- Hopf bifurcation in the presence of symmetry
This page was built for publication: Coupled nonlinear oscillators and the symmetries of animal gaits
