Related papers: A Dynamical Systems Approach to Cryptocurrency Sta…
This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The nominal system is a linear quantum system defined by a linear vector of…
In this paper we consider a system coupling a wave equation with a heat equation through its boundary conditions. The existence of a small parameter in the heat equation, as a factor multiplying the time derivative, implies the existence of…
In this article, we study finite dynamical systems defined over graphs, where the functions are applied asynchronously. Our goal is to quantify and understand stability of the dynamics with respect to the update sequence, and to relate this…
What happens to mining when the Bitcoin price changes, when there are mining supply shocks, the price of energy changes, or hardware technology evolves? We give precise answers based on the technical forces and incentives in the system. We…
The paper discusses various practical consequences of treating economics and finance as an inherently dynamic and chaotic system. On the theoretical side this looks at the general applicability of the market-making pricing approach to…
Regulatory frameworks are a common tool in governance to incent and coerce behaviors supporting national or strategic stability. This includes domestic regulations and international agreements. Though regulation is always a challenge, the…
The theory of the effect of external fluctuation force on the stability and spatial distribution of mutually interacting and slowly evaporating charged drops, levitated in an electrodynamic balance, is presented using classical…
This paper presents a non-linear stability analysis for dc-microgrids in both, interconnected mode and island operation with primary control. The proposed analysis is based on the fact that the dynamical model of the grid is a gradient…
When a system has more than one stable state, how can the stability of these states be compared? This deceptively simple question has important consequences for ecosystems, because systems with alternative stable states can undergo dramatic…
This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…
Blockchain technology relies on decentralization to resist faults and attacks while operating without trusted intermediaries. Although industry experts have touted decentralization as central to their promise and disruptive potential, it is…
We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations). We develop a general approach, based on…
This paper is concerned with the stability of shares in a cryptocurrency where the new coins are issued according to the Proof of Stake protocol. We identify large, medium and small investors under various rewarding schemes, and show that…
Stablecoins are a class of cryptocurrencies which aim at providing consistency and predictability, typically by pegging the token's value to that of a real world asset. Designing resilient decentralized stablecoins is a challenge, and…
We consider the problem of estimating a vector of unknown constant parameters for a class of hybrid dynamical systems -- that is, systems whose state variables exhibit both continuous (flow) and discrete (jump) evolution. Using a hybrid…
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…
There are two main approaches to non-equlibrium statistical mechanics: one using stochastic processes and the other using dynamical systems. To model the dynamics during inflation one usually adopts a stochastic description, which is known…
A comparative study of thawing and tracking models of dark energy is carried out with the help of a dynamical systems analysis. It is found that both of them have stable solutions which are consistent with the requirement of a dark energy.…
With emergence of blockchain technologies and the associated cryptocurrencies, such as Bitcoin, understanding network dynamics behind Blockchain graphs has become a rapidly evolving research direction. Unlike other financial networks, such…
We carry out a general study of the stability of astrophysical flows that appear steady in a uniformly rotating frame. Such a flow might correspond to a stellar pulsation mode or an accretion disk with a free global distortion giving it…