Related papers: A Graphical-Based Method for Plotting Local Bifurc…
Spectral bifurcation diagrams (SBDs) have recently emerged as an efficient tool for identifying dynamical transitions in nonlinear systems through frequency-domain analysis. Previous studies have been limited to numerical investigations,…
Bifurcation equations, non-degeneracy and transversality conditions are obtained for the fold, transcritical, pitchfork and flip bifurcations for periodic points of one dimensional implicitly defined discrete dynamical systems. The backward…
We consider the problem of classifying a map using a team of communicating robots. It is assumed that all robots have localized visual sensing capabilities and can exchange their information with neighboring robots. Using a graph…
Many graph-based learning problems can be cast as finding a good set of vertices nearby a seed set, and a powerful methodology for these problems is based on maximum flows. We introduce and analyze a new method for locally-biased…
The object-oriented class is, in general, the most utilized element in programming and modeling. It is employed throughout the software development process, from early domain analysis phases to later maintenance phases. A class diagram…
Area preserving maps provide the simplest and most accurate means to visualize and quantify the behavior of nonlinear systems. Convenience of the mapping equations of motion for investigation of transition to chaotic behavior in dynamics of…
As digitization in engineering progressed, circuit diagrams (also referred to as schematics) are typically developed and maintained in computer-aided engineering (CAE) systems, thus allowing for automated verification, simulation and…
The central nervous system is composed of many individual units -- from cells to areas -- that are connected with one another in a complex pattern of functional interactions that supports perception, action, and cognition. One natural and…
There is growing interest in anticipating critical transitions in natural systems, often pursued through statistical detection of early warning signals associated with dynamical bifurcations. In stochastic dynamical systems, such signals…
Locally-biased graph algorithms are algorithms that attempt to find local or small-scale structure in a large data graph. In some cases, this can be accomplished by adding some sort of locality constraint and calling a traditional graph…
We numerically study some of the 3-D dynamical systems which exhibit complete synchronisation as well as generalised synchronisation (GS) to show that these systems can be conveniently partitioned into equivalent classes facilitating the…
We present Decapodes, a diagrammatic tool for representing, composing, and solving partial differential equations. Decapodes provides an intuitive diagrammatic representation of the relationships between variables in a system of equations,…
A local algorithm is a distributed algorithm that completes after a constant number of synchronous communication rounds. We present local approximation algorithms for the minimum dominating set problem and the maximum matching problem in…
Changes in the parameters of dynamical systems can cause the state of the system to shift between different qualitative regimes. These shifts, known as bifurcations, are critical to study as they can indicate when the system is about to…
A machine-learning strategy for investigating the stability of fluid flow problems is proposed herein. The goal is to provide a simple yet robust methodology to find a nonlinear mapping from the parametric space to an indicator representing…
The first step in investigating fractional difference maps, which do not have periodic points except fixed points, is to find asymptotically periodic points and bifurcation points and draw asymptotic bifurcation diagrams. Recently derived…
The goal of this paper is to investigate the importance of providing visual "big pictures" in the teaching of economics. The plurality and variety of concepts, variables, diagrams, and models involved in economics can be a source of…
This paper addresses questions regarding controllability for `generic parameter' dynamical systems, i.e. the question whether a dynamical system is `structurally controllable'. Unlike conventional methods that deal with structural…
Graph embedding algorithms are used to efficiently represent (encode) a graph in a low-dimensional continuous vector space that preserves the most important properties of the graph. One aspect that is often overlooked is whether the graph…
Understanding the dynamical processes that govern the performance of functional materials is essential for the design of next generation materials to tackle global energy and environmental challenges. Many of these processes involve the…