Related papers: Realizing Saddle-Node Bifurcations from Finite Dat…
This paper derives new results for the analysis of nonlinear systems by extending contraction theory in the framework of vector distances. A new tool, vector contraction analysis utilizing a notion of the vector-valued norm which evidently…
A common external forcing can cause a saddle-node bifurcation in an ensemble of identical Duffing oscillators by breaking the symmetry of the individual bistable (double-well) unit. The strength of the forcing determines the separation…
We provide a systematic study of equilibria of contact vector fields and the bifurcations that occur generically in 1-parameter families, and express the conclusions in terms of the Hamiltonian functions that generate the vector fields.…
Satisfaction of the strict saddle property has become a standard assumption in non-convex optimization, and it ensures that many first-order optimization algorithms will almost always escape saddle points. However, functions exist in…
We revisit the smooth convex-concave bilinearly-coupled saddle-point problem of the form $\min_x\max_y f(x) + \langle y,\mathbf{B} x\rangle - g(y)$. In the highly specific case where each of the functions $f(x)$ and $g(y)$ is either affine…
By their nature it is difficult to differentiate chaotic dynamical systems through measurement. In recent years, work has begun on using methods of Topological Data Analysis (TDA) to qualitatively type dynamical data by approximating the…
We show bifurcation of localized spike solutions from spatially constant states in systems of nonlocally coupled equations in the whole space. The main assumptions are a generic bifurcation of saddle-node or transcritical type for spatially…
This study employs scientific machine learning to identify transient time series of dynamical systems near a fold bifurcation of periodic solutions. The unique aspect of this work is that a convolutional neural network (CNN) is trained with…
In this paper, we focus on solving a class of constrained non-convex non-concave saddle point problems in a decentralized manner by a group of nodes in a network. Specifically, we assume that each node has access to a summand of a global…
A sequence of bifurcations is studied in a one-dimensional pattern forming system subject to the variation of two experimental control parameters: a dimensionless electrical forcing number ${\cal R}$ and a shear Reynolds number ${\rm Re}$.…
In this article we construct the parameter region where the existence of a homoclinic orbit to a zero equilibrium state of saddle type in the Lorenz-like system will be analytically proved in the case of a nonnegative saddle value. Then,…
This work proposes a new formulation to the long-standing problem of convex decomposition through learning feature fields, enabling the first feed-forward model for open-world convex decomposition. Our method produces high-quality…
A saddle-node bifurcation cascade is studied in the logistic equation, whose bifurcation points follow an expression formally identical to the one given by Feigenbaum for period doubling cascade. The Feigenbaum equation is generalized…
Bifurcations mark qualitative changes of long-term behavior in dynamical systems and can often signal sudden ("hard") transitions or catastrophic events (divergences). Accurately locating them is critical not just for deeper understanding…
A formal theory of simplicity is introduced, in the context of a "combinational" computation model that views computation as comprising the iterated transformational and compositional activity of a population of agents upon each other.…
We study the asymptotics, box dimension, and Minkowski content of trajectories of some discrete dynamical systems. We show that under very general conditions, trajectories corresponding to parameters where saddle-node bifurcation appears…
We propose a derivative-free saddle-search algorithm designed to locate transition states using only function evaluations. The algorithm employs a nested architecture consisting of an inner eigenvector search and an outer saddle-point…
Vector field guided path following (VF-PF) algorithms are fundamental in robot navigation tasks, but may not deliver the desirable performance when robots encounter singular points where the vector field becomes zero. The existence of…
Automata networks can be seen as bare finite dynamical systems, but their growing theory has shown the importance of the underlying communication graph of such networks. This paper tackles the question of what dynamics can be realized up to…
In this paper we introduce a new method which employs the concept of "Orientation Vectors" to train a feed forward neural network and suitable for problems where large dimensions are involved and the clusters are characteristically sparse.…