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. …”
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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.…”
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Study on Dynamics Characteristic of High Speed Herringbone Gear Transmission System by Yongchao Yuan, Ziling Wang, Zhongming Liu, Jizhe Mao, Haiming Gang

“…Based on the finite element numerical analysis method， the dynamics equation of herringbone gear transmission system is given and the model of rotor-bearing-gear dynamics system is established. The influence of shear， bending， torsion， axial force， gyroscopic effect and internal damping of rotor shaft are considered in the modeling process， and the influence of time-varying mesh stiffness and transmission error of herringbone gear pair is also considered. …”
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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. …”
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Study on chaos phase space synchronous rotation and distinguish switching security communication by Guang-ming SUN, Jin-jie HUANG

“…A new chaotic dynamic system was proposed and the dynamic of this system was analyzed.Through the research of balance point,Lyapunov index,Lyapunov dimension and Poincare section,the chaotic behavior of the system was approved.Z axis of chaos system phase space was researched.Z axis rotation model in the phase space was built through introducing rotation matrix,and chaos system space synchronous rotation was researched.Based on the research results above,a chaotic distinguish switching security communication system was presented for the communication of information security.…”
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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. …”
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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. …”
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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. …”
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Gravitational Algebras and Applications to Nonequilibrium Physics by Michele Cirafici

“…Additionally, we provide a brief overview of the theory of nonequilibrium dynamical systems in finite dimensions and discuss its generalization to gravitational algebras. …”
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Approximate Prediction-Based Control Method for Nonlinear Oscillatory Systems with Applications to Chaotic Systems by Thiago P. Chagas, Pierre-Alexandre Bliman, Karl H. Kienitz

“…The approximate Prediction-Based Control method (aPBC) is the continuous-time version of the well-known Prediction-Based Chaos Control method applied to stabilize periodic orbits of nonlinear dynamical systems. The method is based on estimating future states of the free system response of continuous-time systems using the solution from the Runge-Kutta implicit method in real time. …”
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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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Physiologically Based Structure of Mean Residence Time by Mária Durišová

“…Therefore, tools from the theory of linear dynamic systems were used for the structural identification of MRT in this study. …”
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The Gauge Integral Theory in HOL4 by Zhiping Shi, Weiqing Gu, Xiaojuan Li, Yong Guan, Shiwei Ye, Jie Zhang, Hongxing Wei

“…The integral is one of the most important foundations for modeling dynamical systems. The gauge integral is a generalization of the Riemann integral and the Lebesgue integral and applies to a much wider class of functions. …”
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Dynamics of Stochastic Coral Reefs Model with Multiplicative Nonlinear Noise by Zaitang Huang

“…Little seems to be known about the ergodicity of random dynamical systems with multiplicative nonlinear noise. …”
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A Note on the Observability of Temporal Boolean Control Network by Wenping Shi, Bo Wu, Jing Han

“…Using the semi tensor product of matrices, the temporal Boolean networks can be converted into discrete time linear dynamic systems with time delays. Then, necessary and sufficient conditions on the observability via two kinds of inputs are obtained. …”
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Condition Monitoring of Gearbox based on Scaling Analysis of Increment Time Series by Lin Jinshan

“…Gearboxes are complex dynamics system,and the dynamics evolving process of a gearbox is hard to describe.The scaling crossover property of increment series of vibration data of gearbox is analyzed,and on this basis,an intrinsic relation between coordinates of starting and ending points of a scaling range is deduced by trigonometric function.As a result,a novel method for condition monitoring of gearboxes is developed.Moreover,the method is applied to condition monitoring of a realistic gearbox,and comparing with the conventional time domain statistical parameter method,and the effectiveness and superiority of the developed method is proved by the result.…”
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Bifurcation Analysis and Single Traveling Wave Solutions of the Variable-Coefficient Davey–Stewartson System by Tianyong Han, Jiajin Wen, Zhao Li

“…On the one hand, we use the bifurcation theory of planar dynamical systems to draw the phase diagram of the variable-coefficient Davey–Stewartson system. …”
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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. …”
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Solvency Evaluation Model of Insurance Company Based on Stochastic Differential Equation by Kai Wang, Ling Zhu

“…In this paper, from the perspective of capital flow, the insurance company’s capital flow is regarded as a dynamic system, the stochastic differential equations model is established to describe its flow characteristics, and the existence of positive equilibrium point of the system is proved, as well as the conditions of stability at equilibrium point, that is, the requirements of the insurance company’s solvency. …”
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A Class of Approximate Damped Oscillatory Solutions to Compound KdV-Burgers-Type Equation with Nonlinear Terms of Any Order: Preliminary Results by Yan Zhao, Weiguo Zhang

“…By the theory and method of planar dynamical systems, existence conditions and number of bounded traveling wave solutions including damped oscillatory solutions are obtained. …”
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