Related papers: Using Zigzag Persistent Homology to Detect Hopf Bi…
Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically…
The stability theorem for persistent homology is a central result in topological data analysis. While the original formulation of the result concerns the persistence barcodes of $\mathbb{R}$-valued functions, the result was later cast in a…
The conventional wisdom is that a software-defined network (SDN) operates under the premise that the logically centralized control plane has an accurate representation of the actual data plane state. Unfortunately, bugs, misconfigurations,…
Quantifying the stability of an equilibrium is central in the theory of dynamical systems as well as in engineering and control. A comprehensive picture must include the response to both small and large perturbations, leading to the…
Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample---not necessarily a uniform one---of some high-dimensional…
We investigate bifurcation phenomena between slow and fast convergences of synchronization errors arising in the proposed synchronization system consisting of two identical nonlinear dynamical systems linked by a common noisy input only.…
We study the dynamics arising when two identical oscillators are coupled near a Hopf bifurcation where we assume a parameter $\epsilon$ uncouples the system at $\epsilon=0$. Using a normal form for $N=2$ identical systems undergoing Hopf…
Complex systems exhibiting critical transitions when one of their governing parameters varies are ubiquitous in nature and in engineering applications. Despite a vast literature focusing on this topic, there are few studies dealing with the…
We carried out a fluid dynamical simulation for a forced dripping faucet system using a new algorithm that was recently developed. The simulation shows that periodic external forcing induces transitions from chaotic to periodic motion and…
We present a computer-assisted approach to prove the existence of Hopf bubbles and degenerate Hopf bifurcations in ordinary and delay differential equations. We apply the method to rigorously investigate these nonlocal bifurcation…
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…
Sudden and abrupt changes can occur in a nonlinear system within many fields of science when such a system crosses a tipping point and rapid changes of the system occur in response to slow changes in an external forcing. These can occur…
Initially, the logistic map became popular as a simplified model for population growth. In spite of its apparent simplicity, as the population growth-rate is increased the map exhibits a broad range of dynamics, which include bifurcation…
Regulation of zinc uptake in roots of Arabidopsis thaliana has recently been modeled by a system of ordinary differential equations based on the uptake of zinc, expression of a transporter protein and the interaction between an activator…
A data-driven model identification strategy is developed for dynamical systems near a supercritical Hopf bifurcation with nonautonomous inputs. This strategy draws on phase-amplitude reduction techniques, leveraging an analytical…
Motivated by the problem of dealing with incomplete or imprecise acquisition of data in computer vision and computer graphics, we extend results concerning the stability of persistent homology with respect to function perturbations to…
We study fully three-dimensional droplets that slide down an incline by employing a thin-film equation that accounts for capillarity, wettability, and a lateral driving force in small-gradient (or long-wave) approximation. In particular, we…
This paper shows that the variance of load bus voltage magnitude in a small power system test case increases monotonically as the system approaches a Hopf bifurcation. This property can potentially be used as a method for monitoring…
The memory-based diffusion systems have wide applications in practice. Hopf bifurcations are observed from such systems. To meet the demand for computing the normal forms of the Hopf bifurcations of such systems, we develop an effective new…
Open-world video games present a broader search space than other video games, posing challenges for test automation. Fuzzing, which generates new inputs by mutating an initial input, is commonly used to uncover issues. In this study, we…