Computation of the topological entropy in chaotic biophysical bursting models for excitable cells by Jorge Duarte, Luís Silva, J. Sousa Ramos

“…Although there is an elegant interpretation of many experimental results in terms of nonlinear dynamical systems, the dynamics of bursting models is not completely described. …”
Get full text

Chaos in Ecology: The Topological Entropy of a Tritrophic Food Chain Model by Jorge Duarte, Cristina Januário, Nuno Martins

“…This work is still another illustration of the role that the theory of dynamical systems can play in the study of chaotic dynamics in life sciences.…”
Get full text

Tight computationally efficient approximation of matrix norms with applications by Juditsky, Anatoli, Kotsalis, Georgios, Nemirovski, Arkadi

“…Finally, we consider some applications of norm bounding, in particular, (1) computationally efficient synthesis of affine non-anticipative finite-horizon control of discrete time linear dynamical systems under bounds on the peak-to-peak gains, (2) signal recovery with uncertainties in sensing matrix, and (3) identification of parameters of time invariant discrete time linear dynamical systems via noisy observations of states and inputs on a given time horizon, in the case of “uncertain-but-bounded” noise varying in a box.…”
Get full text

Data-driven model discovery and model selection for noisy biological systems. by Xiaojun Wu, MeiLu McDermott, Adam L MacLean

“…We propose a data-driven framework for model discovery and model selection using hybrid dynamical systems: partial models containing missing terms. …”
Get full text

Application of Bifurcation Method to the Generalized Zakharov Equations by Ming Song

“…We use the bifurcation method of dynamical systems to study the traveling wave solutions for the generalized Zakharov equations. …”
Get full text

A chaotic bursting-spiking transition in a pancreatic beta-cells system: observation of an interior glucose-induced crisis by Jorge Duarte, Cristina Januário, Nuno Martins

“…This study provides an illustration of how an integrated approach, involving numerical evidences and theoretical reasoning within the theory of dynamical systems, can directly enhance our understanding of biophysically motivated models.…”
Get full text

Nonlinear modeling of oral glucose tolerance test response to evaluate associations with aging outcomes. by Grant Schumock, Karen Bandeen-Roche, Chee W Chia, Rita R Kalyani, Luigi Ferrucci, Ravi Varadhan

“…We hypothesize that dynamical systems model summaries are predictive of age-related declines in health and function. …”
Get full text

Classification of Human Learning Stages via Kernel Distribution Embeddings by Madeleine Shuhn-Tsuan Yuh, Kendric Ray Ortiz, Kylie Sue Sommer-Kohrt, Meeko Oishi, Neera Jain

“…Our approach is more accurate than standard classification methods, such as nearest centroid assignment, which rely on metrics that are not inherently suited to analysis of trajectories of stochastic dynamical systems.…”
Get full text

New Exact Explicit Nonlinear Wave Solutions for the Broer-Kaup Equation by Zhenshu Wen

“…Many exact explicit expressions of the nonlinear wave solutions for the equation are obtained by exploiting the bifurcation method and qualitative theory of dynamical systems. These solutions contain solitary wave solutions, singular solutions, periodic singular solutions, and kink-shaped solutions, most of which are new. …”
Get full text

Recent applications of fractional calculus to science and engineering by Lokenath Debnath

“…This paper deals with recent applications of fractional calculus to dynamical systems in control theory, electrical circuits with fractance, generalized voltage divider, viscoelasticity, fractional-order multipoles in electromagnetism, electrochemistry, tracer in fluid flows, and model of neurons in biology. …”
Get full text

Topological Entropy of One Type of Nonoriented Lorenz-Type Maps by Guo Feng

“…Constructing a Poincaré map is a method that is often used to study high-dimensional dynamical systems. In this paper, a geometric model of nonoriented Lorenz-type attractor is studied using this method, and its dynamical property is described. …”
Get full text

Second-Order Model Reduction Based on Gramians by Cong Teng

“…Some new and simple Gramian-based model order reduction algorithms are presented on second-order linear dynamical systems, namely, SVD methods. Compared to existing Gramian-based algorithms, that is, balanced truncation methods, they are competitive and more favorable for large-scale systems. …”
Get full text

Some Smooth and Nonsmooth Traveling Wave Solutions for KP-MEW(2, 2) Equation by Liping He, Yuanhua Lin, Hongying Zhu

“…In this paper, we consider the KP-MEW(2, 2) equation by the theory of bifurcations of planar dynamical systems when integral constant is considered. …”
Get full text

A novel conceptual model for Dansgaard–Oeschger event dynamics based on ice-core data by J. O. Melcher, S. Halkjær, P. Ditlevsen, P. L. Langen, G. Vettoretti, S. O. Rasmussen

“…<p>This study introduces a novel dynamical systems model designed to capture the highly non-periodic nature of Dansgaard–Oeschger (DO) events. …”
Get full text

The Weighted Fermat Triangle Problem by Yujin Shen, Juan Tolosa

“…We provide geometric interpretations of the conditions and briefly indicate a connection with dynamical systems.…”
Get full text

Bifurcations of Traveling Wave Solutions for the Coupled Higgs Field Equation by Shengqiang Tang, Shu Xia

“…By using the bifurcation theory of dynamical systems, we study the coupled Higgs field equation and the existence of new solitary wave solutions, and uncountably infinite many periodic wave solutions are obtained. …”
Get full text

Complete Controllability of Impulsive Fractional Linear Time-Invariant Systems with Delay by Xian-Feng Zhou, Song Liu, Wei Jiang

“…This paper is concerned with the complete controllability of impulsive fractional linear time-invariant dynamical systems with delay. The criteria on the controllability of the system, which is sufficient and necessary, are established by constructing suitable control inputs. …”
Get full text

Peakon, Solitary and Smooth Periodic Wave Solutions for a Modification of the K(2,2) Equation by Qing Meng, Bin He

“…We consider a modification of the K(2,2) equation ut=2uuxxx+2kuxuxx+2uux using the bifurcation method of dynamical systems and the method of phase portraits analysis. …”
Get full text

Periodic Wave Solutions and Their Limits for the Generalized KP-BBM Equation by Ming Song, Zhengrong Liu

“…We use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the generalized KP-BBM equation. …”
Get full text

Moment Lyapunov exponent of delay differential equations by M. S. Fofana

“…The aim of this paper is to establish a connecting thread through the probabilistic concepts of pth-moment Lyapunov exponents, the integral averaging method, and Hale's reduction approach for delay dynamical systems. We demonstrate this connection by studying the stability of perturbed deterministic and stochastic differential equations with fixed time delays in the displacement and derivative functions. …”
Get full text