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Phase Locking in Coupled Oscillators as Hybrid Automata


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  • Product Description

Holk Cruse's system-level model of coordination can account for gait transitions in arthropods analogous to: walk, trot, gallop in quadrupeds. It has been adapted to control locomotion in a series of hexapod robots. Gaits emerge from interaction among pairs of legs as effected by simple discrete-event coordination mechanisms, abstracting physiology and dynamics. We represent this model as systems of coupled hybrid dynamic oscillators. Gaits are quantified by a discrete phase vector. Using numerical and symbolic Monte Carlo simulations, synchronization of coupled oscillators networks can be studied parametrically. A constructive, section-map approach that exploits the polyhedral geometry is developed. Periodic orbits, their domains of admissibility and stability, as well as expressions for the period of oscillation and relative phases can be computed. For 2-oscillator networks, we observe agreement with simulation results. Analysis of larger networks may benefit from consideration of Virtual Periodic Orbits, defined on the affine hull of the original dynamics. Virtual orbits are canonical precursors for a class of non-smooth bifurcations and predictive of long transient behavior.

Product Specifications
SKU :COC93662
AuthorAlan Calvitti
Number of Pages232
Publishing Year2011-11-15T00:00:00.000
Edition1 st
Book TypeMathematics
Country of ManufactureIndia
Product BrandLAP LAMBERT Academic Publishing
Product Packaging InfoBox
In The Box1 Piece
Product First Available On ClickOnCare.com2015-08-14 00:00:00