Related papers: Stability threshold approach for complex dynamical…

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…

Multistability is a phenomenon prevalent in many natural systems. In climate, for example, it allows the possibility of irreversible consequences on planetary scale as a result of climate change. Indeed, a climate ``tipping element'' is a…

Control systems can show robustness to many events, like disturbances and model inaccuracies. It is natural to speculate that they are also robust to sporadic deadline misses when implemented as digital tasks on an embedded platform. This…

We extend the notion of estimation entropy of autonomous dynamical systems proposed by Liberzon and Mitra [1] to nonlinear dynamical systems with uncertain inputs with bounded variation. We call this new notion the {$\epsilon$}-estimation…

We describe the notion of stability of coherent systems as a framework to deal with redundancy. We define stable coherent systems and show how this notion can help the design of reliable systems. We demonstrate that the reliability of…

Motivation: Many biochemical pathways are known, but the numerous parameters required to correctly explore the dynamics of the pathways are not known. For this reason, algorithms that can make inferences by looking at the topology of a…

In modern power systems, the operating point, at which the demand and supply are balanced, may take different values due to changes in loads and renewable generation levels. Understanding the dynamics of stressed power systems with a range…

Stability is an important aspect of a classification procedure because unstable predictions can potentially reduce users' trust in a classification system and also harm the reproducibility of scientific conclusions. The major goal of our…

In this work, we develop an analytical framework to understand quantum friction across distinct stability regimes, providing approximate expressions for frictional forces both in the deep stable regime and near the critical threshold of…

Stochastic Thermodynamics (ST) extends the notions of classical thermodynamics to trajectories taken from a nonequilibrium ensemble. This extension yields a simple approach to fluctuation relations in small systems. Multiple time- and…

In this paper, we analyze the generalization performance of the Iterative Hard Thresholding (IHT) algorithm widely used for sparse recovery problems. The parameter estimation and sparsity recovery consistency of IHT has long been known in…

This paper proves an instability theorem for dynamical systems. As one adds interactions between subystems in a complex system, structured or random, a threshold of connectivity is reached beyond which the overall dynamics inevitably goes…

Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially…

We aim to increase the ability of a of coupled phase oscillators to maintain the synchronization when the system is affected by stochastic disturbances. We model the disturbances by Gaussian noise and use the mean first hitting time when…

We propose a computational framework to quantify (measure) and to optimize the reliability of complex systems. The approach uses a graph representation of the system that is subject to random failures of its components (nodes and edges).…

This paper studies robustness of MIMO control systems with parametric uncertainties, and establishes a lower dimensional robust stability criterion. For control systems with interval transfer matrices, we identify the minimal testing set…

This thesis consists of two separate parts: in each we study the stability under small perturbations of certain probability models in different contexts. In the first, we study small random perturbations of a deterministic dynamical system…

For constrained system which has several independent first integrals, we give a new stabilization method which named adjustment-stabilization method. It can stabilize all known constants of motion for a given dynamical system very well…

We present a method for the steady state optimization of nonlinear delay differential equations. The method ensures stability and robustness, where a system is called robust if it remains stable despite uncertain parameters. Essentially, we…

This paper is concerned with a robust instability analysis for the single-input-single-output unstable linear time-invariant (LTI) system under dynamic perturbations. The nominal system itself is possibly perturbed by the static gain of the…