Solutions to All-Colors Problem on Graph Cellular Automata by Xiaoyan Zhang, Chao Wang

“…The All-Ones Problem comes from the theory of σ+-automata, which is related to graph dynamical systems as well as the Odd Set Problem in linear decoding. …”
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Design of a Dynamic Simulator for a Biped Robot by Diego A. Bravo M, Carlos F. Rengifo Rodas

“…Simulation is a virtual representation of a dynamic system. For the case of mechanical systems, the simulator is used to calculate the reaction forces between its base and the ground and other constraints. …”
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Pour une grille de lecture scientifique des sites web par les géographes by Henry Bakis, Sabrina Marchandise, Joy Raynaud, Jérémie Valentin

“…By a consistent and rigorous analysis of websites, this methodological grid will thus improve the understanding of a dynamic system of actors, territories and networks in research.…”
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New Exact Solitary Wave Solutions of a Coupled Nonlinear Wave Equation by XiaoHua Liu, CaiXia He

“…By using the theory of planar dynamical systems to a coupled nonlinear wave equation, the existence of bell-shaped solitary wave solutions, kink-shaped solitary wave solutions, and periodic wave solutions is obtained. …”
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Traveling Wave Solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony Equation by Zhengyong Ouyang

“…We use bifurcation method of dynamical systems to study exact traveling wave solutions of a nonlinear evolution equation. …”
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An Analysis of the Replicator Dynamics for an Asymmetric Hawk-Dove Game by Ikjyot Singh Kohli, Michael C. Haslam

“…We analyze, using a dynamical systems approach, the replicator dynamics for the asymmetric Hawk-Dove game in which there is a set of four pure strategies with arbitrary payoffs. …”
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The Existence of Cone Critical Point and Common Fixed Point with Applications by Wei-Shih Du

“…We first establish some new critical point theorems for nonlinear dynamical systems in cone metric spaces or usual metric spaces, and then we present some applications to generalizations of Dancš-Hegedüs-Medvegyev's principle and the existence theorem related with Ekeland's variational principle, Caristi's common fixed point theorem for multivalued maps, Takahashi's nonconvex minimization theorem, and common fuzzy fixed point theorem. …”
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Active stabilization of a chaotic urban system by Günter Haag, Tilo Hagel, Timm Sigg

“…A new method to stabilize dynamical systems by forcing the system variables into the desired unstable stationary point is proposed. …”
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Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability by Manuel De la Sen, Asier Ibeas

“…Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems.…”
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Observer-Based Robust Passive Control for a Class of Uncertain Neutral Systems: An Integral Sliding Mode Approach by Ruiping Xu, Zhen Liu, Cunchen Gao, Huimin Xiao

“…By employing a novel sliding functional, a new sufficient criterion of robust asymptotic stability and passivity for both the error system and the sliding mode (SM) dynamic system is derived via linear matrix inequality (LMI) technique. …”
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Differences and Similarities: Variability and Fractality in CDST by Zhizi Chen

“… Variability and fractality, two key concepts in Complex Dynamic Systems Theory (CDST)—the former concerning changes and variations, and the latter concerning recursiveness and self-similarities—may seem contradictory at first glance. …”
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Bifurcation Approach to Analysis of Travelling Waves in Nonlocal Hydrodynamic-Type Models by Jianping Shi, Jibin Li

“…We apply the method of dynamical systems to investigate the bifurcations of phase portraits depending on the parameters of systems and analyze the dynamical behavior of the travelling wave solutions. …”
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Chaotic Dynamics Analysis Based on Financial Time Series by Zheng Gu, Yuhua Xu

“…Firstly, the nonlinear characteristics of the data are discussed through the empirical analysis of agriculture index data; the daily agriculture index returns can be decomposed into the different scales based on wavelet analysis. Secondly, the dynamic system of some nonlinear characteristic data is established according to the Taylor series expansion form, and the corresponding dynamic characteristics are analyzed. …”
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Grazing Orbits and Related Local Bifurcations of an Oscillator with Continuous and Piecewise-Linear Restoring Force by Haiyan Hu

“…Then, through a brief analysis, the article shows that the grazing phenomenon turns the stability trend of the periodic orbit so abruptly that it may be impossible to predict an incident local bifurcation with the variation of a control parameter from the concept of smooth dynamic systems. The numerical simulation in the article well supports the scheme and the analysis, and shows an abundance of grazing phenomena in an engineering range of the excitation frequency.…”
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Spatio-temporal patterns with hyperchaotic dynamics in diffusively coupled biochemical oscillators by Gerold Baier, Sven Sahle

“…We present three examples how complex spatio-temporal patterns can be linked to hyperchaotic attractors in dynamical systems consisting of nonlinear biochemical oscillators coupled linearly with diffusion terms. …”
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Integrity Design for Networked Control Systems with Actuator Failures and Data Packet Dropouts by Xiaomei Qi, Jason Gu

“…After introducing the matrix of actuator failure, the closed-loop NCS is developed, which can be viewed as asynchronous dynamical systems (ADSs). Then, the sufficiency of exponential stability for the NCS is obtained based on the theory of ADSs. …”
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Position Tracking Control for Permanent Magnet Linear Motor via Continuous-Time Fast Terminal Sliding Mode Control by Wei Gao, Xiuping Chen, Haibo Du, Song Bai

“…Specifically, first, for the second-order model of position error dynamic system, a new continuous-time fast terminal sliding surface is introduced and an improved continuous-time fast terminal sliding mode control law is proposed. …”
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On the derivation of the nonlinear discrete equations numerically integrating the Euler PDEs by F. N. Koumboulis, M. G. Skarpetis, B. G. Mertzios

“…The Euler equations, namely a set of nonlinear partial differential equations (PDEs), mathematically describing the dynamics of inviscid fluids are numerically integrated by directly modeling the original continuous-domain physical system by means of a discrete multidimensional passive (MD-passive) dynamic system, using principles of MD nonlinear digital filtering. …”
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Dynamical behavior analysis and traveling wave solution of stochastic Riemann wave equations by Jie Luo, Jiangtao Guo, Yan Shao, Guangxu Zhao, Min Jiao

“…Finally, two-dimensional planar dynamical systems and its disturbance systems are considered by using Mathematical software. …”
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Consilience of Reductionism and Complexity Theory in Language Research: Adaptive Weight Model by Chao Zhang

“…This paper starts by discussing the adaptability of complex dynamic systems and combines cognitive processing model and artificial neural networks to construct and verify an adaptive weight model, showing that the study of reductionism is induction of high-weight elements and the study of complexity theory is a discussion of system complexity from adaptability, meaning that there is a good fit between the two frameworks. …”
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