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With the tracking condition, the stability of quintessence solutions are examined. It is found that there is only one physically relevant fixed point for the system generically. Two specific examples of quintessence potentials are worked…
We show that for isolated relativistic systems with spin the conservation of total angular momentum implies that, instead of the center of mass, it is a modified center of mass and spin which behaves inertially. This requires a change in…
In this paper, we study the emergence of circular formation for agents in cyclic pursuit. Each agent is a unicycle traveling at a fixed common forward speed. We first establish a necessary and sufficient condition for the existence of…
Mass action systems capture chemical reaction networks in homogeneous and dilute solutions. We suggest a notion of generalized mass action systems that admits arbitrary nonnegative power-law rate functions and serves as a more realistic…
The study on the stability of relativistic disks is one of the most important criteria for the characterization of astrophysically relevant galactic or accretion disks models. In this paper, we perform an analysis of the stability of static…
A natural condition on the structure of the underlying chemical reaction network, namely weak reversibility, is shown to guarantee the existence of an equilibrium (steady state) in each positive stoichiometric compatibility class for the…
We study a class of matrices with a rank-1 interconnection structure, and derive a simple necessary and sufficient condition for diagonal stability. The underlying Lyapunov function is used to provide sufficient conditions for diagonal…
Stability guarantees are crucial when ensuring a fully autonomous robot does not take undesirable or potentially harmful actions. Unfortunately, global stability guarantees are hard to provide in dynamical systems learned from data,…
Recent experimental results based on multi-electrode and imaging techniques have reinvigorated the idea that large neural networks operate near a critical point, between order and disorder. However, evidence for criticality has relied on…
Robustness guarantees are important properties to be looked for during control design. They ensure stability of closed-loop systems in face of uncertainties, unmodeled effects and bounded disturbances. While the theory on robust stability…
The Cauchy problem for the attraction-repulsion chemotaxis system in the whole $n$-dimensional space has uncountable constant steady states. In the attraction chemotaxis system, each positive constant steady state is stable if it is in a…
In a multi-agent system, unconditional (multiple) consensus is the property of reaching to (multiple) consensus irrespective of the instant and values at which states are initialized. For linear algorithms, occurrence of unconditional…
We prove the nonlinear local stability of Dirac masses for a kinetic model of alignment of particles on the unit sphere, each point of the unit sphere representing a direction. A population concentrated in a Dirac mass then corresponds to…
We re-visit the global - relative to control policies - stability of multiclass queueing networks. In these, as is known, it is generally insufficient that the nominal utilization at each server is below 100%. Certain policies, although…
Motivated by studies on fully discrete numerical schemes for linear hyperbolic conservation laws, we present a framework on analyzing the strong stability of explicit Runge-Kutta (RK) time discretizations for semi-negative autonomous linear…
We consider Activated Random Walk (ARW), a particle system with mass conservation, on the cycle $\mathbb{Z}/n\mathbb{Z}$. One starts with a mass density $\mu>0$ of initially active particles, each of which performs a simple symmetric random…
This paper presents a new condition for the existence of optimal stationary policies in average-cost continuous-time Markov decision processes with unbounded cost and transition rates, arising from controlled queueing systems. This…
The present paper studies existence and distributional uniqueness of subclasses of stationary hard-core particle systems arising as thinnings of stationary particle processes. These subclasses are defined by natural maximality criteria. We…
While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…
Kinetically constrained spin systems play an important role in understanding key properties of the dynamics of slowly relaxing materials, such as glasses. So far kinetic constraints have been introduced in idealised models aiming to capture…