Stability of Steady States with Complex Behavior in Time

Stability of Steady States for Thin Film

Basin stability measure of different steady states in coupled oscillators

In this report, we investigate the stabilization of saddle fixed points in coupled oscillators where individual oscillators exhibit the saddle fixed points. The coupled oscillators may have two structurally different types of suppressed states, namely amplitude death and oscillation death. The stabilization of saddle equilibrium point refers to the amplitude death state where oscillations are c...

On the Stability of Steady States in a Granuloma Model

We consider a free boundary problem for a system of two semilinear parabolic equations. The system represents a simple model of granuloma, a collection of immune cells and bacteria filling a 3dimensional domain Ω(t) which varies in time. We prove the existence of stationary spherical solutions and study their linear asymptotic stability as time increases to infinity.

Flat steady states in stellar dynamics—existence and stability

We consider a special case of the three dimensional Vlasov-Poisson system where the particles are restricted to a plane, a situation that is used in astrophysics to model extremely flattened galaxies. We prove the existence of steady states of this system. They are obtained as minimizers of an energy-Casimir functional from which fact a certain dynamical stability property is deduced. From a ma...

Node Balanced Steady States: Unifying and Generalizing Complex and Detailed Balanced Steady States.

We introduce a unifying and generalizing framework for complex and detailed balanced steady states in chemical reaction network theory. To this end, we generalize the graph commonly used to represent a reaction network. Specifically, we introduce a graph, called a reaction graph, that has one edge for each reaction but potentially multiple nodes for each complex. A special class of steady state...