Stability of Poisson Equilibria and Hamiltonian Relative Equilibria by Energy Methods

Stability of Poisson Equilibria and Hamiltonian Relative Equilibria by Energy Methods

We develop a general stability theory for equilibrium points of Poisson dynamical systems and relative equilibria of Hamiltonian systems with symmetries, including several generalisations of the Energy-Casimir and Energy-Momentum Methods. Using a topological generalisation of Lyapunov’s result that an extremal critical point of a conserved quantity is stable, we show that a Poisson equilibrium ...

Stability of Hamiltonian Relative Equilibria by Energy Methods

Asymptotic and Lyapunov stability of Poisson equilibria

This paper includes results centered around three topics, all of them related with the nonlinear stability of equilibria in Poisson dynamical systems. Firstly, we prove an energy-Casimir type sufficient condition for stability that uses functions that are not necessarily conserved by the flow and that takes into account certain asymptotically stable behavior that may occur in the Poisson catego...

Persistence and Stability of Relative Equilibria

We consider relative equilibria in symmetric Hamiltonian systems, and their persistence or bifurcation as the momentum is varied. In particular, we extend a classical result about persistence of relative equilibria from values of the momentum map that are regular for the coadjoint action, to arbitrary values, provided that either (i) the relative equilibrium is at a local extremum of the reduce...

stability and attraction domains of traffic equilibria in day-to-day dynamical system formulation

در این پژوهش مسئله واگذاری ترافیک را از دید سیستم های دینامیکی فرمول بندی می کنیم.فرض کرده ایم که همه فاکتورهای وابسته در طول زمان ثابت باشند و تعادل کاربر را از طریق فرایند منظم روزبه روز پیگیری کنیم.دینامیک ترافیک توسط یک نگاشت بازگشتی نشان داده می شود که تکامل سیستم در طول زمان را نشان می دهد.پایداری تعادل و دامنه جذب را توسط مطالعه ویژگی های توپولوژیکی تکامل سیستم تجزیه و تحلیل می کنیم.پاید...