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

Stability of Stochastic Differential Delay Systems with Delayed Impulses by Yanlei Wu

“…Moreover, it is also shown that if a continuous dynamic system is stable, then, under some conditions, the delayed impulses do not destroy the stability of the systems. …”
Get full text

Peakon, Cuspon, Compacton, and Loop Solutions of a Three-Dimensional 3DKP(3, 2) Equation with Nonlinear Dispersion by Haixia Zhao, Lijing Qiao, Shengqiang Tang

“…Based on the method of dynamical systems, the 3DKP(3,2) equation is shown to have the parametric representations of the solitary wave solutions such as peakon, cuspon, compacton, and loop solutions. …”
Get full text

Large-Eddy Simulation of the Flow Past a Circular Cylinder at Re = 130,000: Effects of Numerical Platforms and Single- and Double-Precision Arithmetic by Dmitry A. Lysenko

“…The reconstructed attractors of the dynamic systems in phase space are limited by an ellipsoid.…”
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

A Panoramic Sketch about the Robust Stability of Time-Delay Systems and Its Applications by Baltazar Aguirre-Hernández, Raúl Villafuerte-Segura, Alberto Luviano-Juárez, Carlos Arturo Loredo-Villalobos, Edgar Cristian Díaz-González

“…This paper presents a brief review on the current applications and perspectives on the stability of complex dynamical systems, with an emphasis on three main classes of systems such as delay-free systems, time-delay systems, and systems with uncertainties in its parameters, which lead to some criteria with necessary and/or sufficient conditions to determine stability and/or stabilization in the domains of frequency and time. …”
Get full text

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. …”
Get full text

Random Attractors for Stochastic Retarded 2D-Navier-Stokes Equations with Additive Noise by Xiaoyao Jia, Xiaoquan Ding

“…Then conjugation relation between two random dynamical systems implies the existence of a random attractor for the stochastic equation. …”
Get full text

Travelling Wave Solutions of Nonlinear Dynamical Equations in a Double-Chain Model of DNA by Zheng-yong Ouyang, Shan Zheng

“…By using the method of dynamical systems, the bounded traveling wave solutions such as bell-shaped solitary waves and periodic waves for the coupled nonlinear dynamical equations of DNA model are obtained and simulated numerically. …”
Get full text

Travelling wave solutions for higher-order wave equations of KDV type (III) by Jibin Li, Weigou Rui, Yao Long, Bin He

“…By using the theory of planar dynamical systems to the travellingwave equation of a higher order nonlinear wave equations of KdV type, theexistence of smooth solitary wave, kink wave and anti-kink wave solutions anduncountably infinite many smooth and non-smooth periodic wave solutions areproved. …”
Get full text

Periodic and Solitary-Wave Solutions for a Variant of the K(3,2) Equation by Jiangbo Zhou, Lixin Tian

“…We employ the bifurcation method of planar dynamical systems and qualitative theory of polynomial differential systems to derive new bounded traveling-wave solutions for a variant of the K(3,2) equation. …”
Get full text

Double Weak Hopf Quiver and Its Path Coalgebra by Muhammad Naseer Khan, Munir Ahmed, Muhammad Arshad, Waleed Almutiry, Rashad A. R. Bantan, Mohammed Elgarhy

“…These structures are important in the physics for dynamic systems.…”
Get full text

Data Dependence, Strict Fixed Point Results, and Well-Posedness of Multivalued Weakly Picard Operators by Azhar Hussain, Ahsan Ali, Vahid Parvaneh, Hassen Aydi

“…To show the usability of our results, we give some examples and an application to resolve a functional equation arising in dynamical systems.…”
Get full text

Estimation of initial functions for systems with delays from discrete measurements by Krzysztof Fujarewicz

“…The work presents a gradient-based approach to estimation of initial functions of time delay elements appearing in models of dynamical systems. It is shown how to generate the gradient of the estimation objective function in the initial function space using adjoint sensitivity analysis. …”
Get full text

A novel approach to Lyapunov stability of Caputo fractional dynamic equations on time scale using a new generalized derivative by Michael Precious Ineh, Edet Peter Akpan, Hossam A. Nabwey

“…The results presented in this work contributed to the broader understanding of fractional calculus on time scales, enriching the theoretical foundation of dynamic systems analysis. Illustrative examples were included to demonstrate the effectiveness, relevance, and practical applicability of the established stability and asymptotic stability results. …”
Get full text

Delta-Nabla Type Maximum Principles for Second-Order Dynamic Equations on Time Scales and Applications by Jiang Zhu, Dongmei Liu

“…By using these maximum principles, the uniqueness theorems of the solutions, the approximation theorems of the solutions, the existence theorem, and construction techniques of the lower and upper solutions for second-order linear and nonlinear initial value problems and boundary value problems on time scales are proved, the oscillation of second-order mixed delat-nabla differential equations is discussed and, some maximum principles for second order mixed forward and backward difference dynamic system are proved.…”
Get full text

Periodic Solution of Prey-Predator Model with Beddington-DeAngelis Functional Response and Impulsive State Feedback Control by Chunjin Wei, Lansun Chen

“…By using the geometry theory of semicontinuous dynamic system and the method of successor function, we obtain the system with impulsive effects that has an order one periodic solution, and sufficient conditions for existence and stability of order one periodic solution are also obtained. …”
Get full text

Robust Stability of a Class of Uncertain Lur'e Systems of Neutral Type by W. Weera, P. Niamsup

“…We analyze the global exponential stability for uncertain neutral and Lur’e dynamical systems with some sector conditions. By constructing a set of improved Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, we establish some stability criteria in terms of linear matrix inequalities. …”
Get full text

Bounded Traveling Wave Solutions and Their Relations for the Generalized HD Type Equation by Qing Meng, Bin He

“…The generalized HD type equation is studied by using the bifurcation method of dynamical systems. From a dynamic point of view, the existence of different kinds of traveling waves which include periodic loop soliton, periodic cusp wave, smooth periodic wave, loop soliton, cuspon, smooth solitary wave, and kink-like wave is proved and the sufficient conditions to guarantee the existence of the above solutions in different regions of the parametric space are given. …”
Get full text

Nonlinear stochastic Markov processes and modeling uncertainty in populations by H.Thomas Banks, Shuhua Hu

“…We consider an alternative approach to the use of nonlinear stochastic Markov processes (which have a Fokker-Planck or Forward Kolmogorov representation for density) in modeling uncertainty in populations.These alternate formulations, which involve imposing probabilistic structures on a family of deterministic dynamical systems, are shown to yield pointwise equivalent population densities. …”
Get full text