W-Stability of Multistable Nonlinear Discrete-Time Systems by Zhishuai Ding, Guifang Cheng, Xiaowu Mu

“…Motivated by the importance and application of discrete dynamical systems, this paper presents a new Lyapunov characterization which is an extension of conventional Lyapunov characterization for multistable discrete-time nonlinear systems. …”
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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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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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Global Stability for Fractional Diffusion Equations in Biological Systems by Khalid Hattaf, Noura Yousfi

“…This paper proposes a new method of construction of Lyapunov functionals for the dynamical systems described by fractional differential equations and fractional partial differential equations. …”
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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. …”
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New Exact Solutions for High Dispersive Cubic-Quintic Nonlinear Schrödinger Equation by Yongan Xie, Shengqiang Tang

“…Applying bifurcation theory of dynamical systems and the Fan sub-equations method, more types of exact solutions, particularly solitary wave solutions, are obtained for the first time.…”
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Existence of Solutions for Fractional Differential Inclusions with Separated Boundary Conditions in Banach Space by Mabrouk Bragdi, Amar Debbouche, Dumitru Baleanu

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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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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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Synchronization between two Hele-Shaw Cells by A. Bernardini, J. Bragard, H. Mancini

“…Complete synchronization between two Hele-Shaw cells is examined.The two dynamical systems are chaotic in time and spatiallyextended in two dimensions. …”
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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. …”
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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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Syntheses of differential games and pseudo-Riccati equations by Yuncheng You

“…For differential games of fixed duration of linear dynamical systems with nonquadratic payoff functionals, it is proved that the value and the optimal strategies as saddle point exist whenever the associated pseudo-Riccati equation has a regular solution P(t,x). …”
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Fixed Points, Symmetries, and Bounds for Basins of Attraction of Complex Trigonometric Functions by Kasey Bray, Jerry Dwyer, Roger W. Barnard, G. Brock Williams

“…The dynamical systems of trigonometric functions are explored, with a focus on tz=tanz and the fractal image created by iterating the Newton map, Ftz, of  tz. …”
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High-Precision Continuation of Periodic Orbits by Ángeles Dena, Marcos Rodríguez, Sergio Serrano, Roberto Barrio

“…Obtaining periodic orbits of dynamical systems is the main source of information about how the orbits, in general, are organized. …”
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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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Application of Piecewise Successive Linearization Method for the Solutions of the Chen Chaotic System by S. S. Motsa, Y. Khan, S. Shateyi

“…The work shows that the proposed method provides good accuracy and can be easily extended to other dynamical systems including those that are chaotic in nature.…”
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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. …”
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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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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. …”
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