ﻻ يوجد ملخص باللغة العربية
We establish the existence of a bifurcation from an attractive random equilibrium to shear-induced chaos for a stochastically driven limit cycle, indicated by a change of sign of the first Lyapunov exponent. This addresses an open problem posed by Kevin Lin and Lai-Sang Young, extending results by Qiudong Wang and Lai-Sang Young on periodically kicked limit cycles to the stochastic context.
Using geometric inversion with respect to the origin we extend the definition of box dimension to the case of unbounded subsets of Euclidean spaces. Alternative but equivalent definition is provided using stereographic projection on the Riemann spher
Microbial electrolysis cells (MECs) are a promising new technology for producing hydrogen cheaply, efficiently, and sustainably. However, to scale up this technology, we need a better understanding of the processes in the devices. In this effort, we
We study the number and distribution of the limit cycles of a planar vector field whose component functions are random polynomials. We prove a lower bound on the average number of limit cycles when the random polynomials are sampled from the Kostlan-
We discuss how matrix-free/timestepper algorithms can efficiently be used with dynamic non-Newtonian fluid mechanics simulators in performing systematic stability/bifurcation analysis. The timestepper approach to bifurcation analysis of large scale s
We seek solutions $uinR^n$ to the semilinear elliptic partial difference equation $-Lu + f_s(u) = 0$, where $L$ is the matrix corresponding to the Laplacian operator on a graph $G$ and $f_s$ is a one-parameter family of nonlinear functions. This arti