Convexity of the Set of Fixed Points Generated by Some Control Systems by Vadim Azhmyakov

“…We study closed-loop and open-loop controllable dynamical systems governed by ordinary differential equations (ODEs) and establish convexity of the set of trajectories. …”
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On Algebraic Approach in Quadratic Systems by Matej Mencinger

“…We use the one-to-one correspondence between homogeneous quadratic dynamical systems and algebra which was originally introduced by Markus in (1960). …”
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Topology in nonlinear extensions of hypernumbers by M. S. Burgin

“…Modern theory of dynamical systems is mostly based on nonlinear differential equations and operations. …”
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Abstract mechanical connection and abelian reconstruction for almost Kähler manifolds by Sergey Pekarsky, Jerrold E. Marsden

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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. …”
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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.…”
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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. …”
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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. …”
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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.…”
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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. …”
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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. …”
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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. …”
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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. …”
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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. …”
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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.…”
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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. …”
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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. …”
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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. …”
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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. …”
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Nonlinear dynamics in psychology by Stephen J. Guastello

“…This article provides a survey of the applications of nonlinear dynamical systems theory to substantive problems encountered in the full scope of psychological science. …”
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