A Prediction-Correction Dynamic Method for Large-Scale Generalized Eigenvalue Problems by Xin-long Luo, Jia-ru Lin, Wei-ling Wu

“…This paper gives a new prediction-correction method based on the dynamical system of differential-algebraic equations for the smallest generalized eigenvalue problem. …”
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Dynamic Analysis and Chaos Control of Bertrand Triopoly Based on Differentiated Products and Heterogeneous Expectations by Liuwei Zhao

“…Therefore, the chaotic behavior of the dynamical system is controlled by time-delay feedback control and the numerical analysis shows that the effective control of the dynamical system can be unstable behavior and the rapid recovery of the market can be stable and orderly.…”
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Abundant Bounded and Unbounded Solitary, Periodic, Rogue-Type Wave Solutions and Analysis of Parametric Effect on the Solutions to Nonlinear Klein–Gordon Model by Mohammad Mobarak Hossain, Alrazi Abdeljabbar, Harun-Or Roshid, Md. Mamunur Roshid, Abu Naim Sheikh

“…This paper exploits the modified simple equation and dynamical system schemes to integrate the Klein–Gordon (KG) model amid quadratic nonlinearity arising in nonlinear optics, quantum theories, and solid state physics. …”
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The Holling Type II Population Model Subjected to Rapid Random Attacks of Predator by Jevgeņijs Carkovs, Jolanta Goldšteine, Kārlis Šadurskis

“…Assuming that the averaged dynamical system is the classic Holling type II population model with asymptotically stable limit cycle, we prove that the dynamics of stochastic model may be approximated with a two-dimensional Gaussian Markov process with unboundedly increasing variances.…”
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Complexity of a Microblogging Social Network in the Framework of Modern Nonlinear Science by Andrey Dmitriev, Vasily Kornilov, Svetlana Maltseva

“…We offer a new model of a microblogging social network as a nonlinear random dynamical system with additive noise in three-dimensional phase space. …”
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Asymptotic -Algebras from -Actions on Higher Rank Graphs by Inhyeop Yi

“…For a dynamical system arising from -action on a higher rank graph with finite vertex set, we show that the semidirect product of the asymptotic equivalence relation groupoid is essentially principal if and only if the -graph satisfies the aperiodic condition. …”
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Random Attractors for Stochastic Three-Component Reversible Gray-Scott System with Multiplicative White Noise by Anhui Gu

“…The paper is devoted to proving the existence of a compact random attractor for the random dynamical system generated by stochastic three-component reversible Gray-Scott system with multiplicative white noise.…”
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The decay of mechanical oscillations in piecewise linear system by Genovaitė Zaksienė

“…The parameters of dynamical system where dynamical damper exists more effectively are determined. …”
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Exponential Attractor for Lattice System of Nonlinear Boussinesq Equation by Min Zhao, Shengfan Zhou

“…We study the lattice dynamical system of a nonlinear Boussinesq equation. We first verify the Lipschitz continuity of the continuous semigroup associated with the system. …”
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Supression of mechanical oscillations in a nonlinear systems with restriction by Genovaitė Zaksienė

“…The parameters of dynamical system where dynamical damper exists more effectively are determined. …”
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Random Attractors for the Stochastic Discrete Long Wave-Short Wave Resonance Equations by Jie Xin, Hong Lu

“…We prove the asymptotic compactness of the random dynamical system and obtain the random attractor.…”
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A Stochastic Weakly Damped, Forced KdV-BO Equation by Guolian Wang

“…We first show that the global solution generates a random dynamical system. By energy type estimates and dispersive properties, we then prove that this system possesses a weak random attractor in the space H1(ℝ).…”
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Bifurcation of Traveling Wave Solutions of the Dual Ito Equation by Xinghua Fan, Shasha Li

“…By using the theory of planar dynamical system, we study the existence of its traveling wave solutions. …”
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Anticontrol of Chaos for a Class of Delay Difference Equations Based on Heteroclinic Cycles Connecting Repellers by Zongcheng Li

“…The controlled system is first reformulated into a high-dimensional discrete dynamical system. Then, a chaotification theorem based on the heteroclinic cycles connecting repellers for maps is established. …”
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Random Attractors for Stochastic Three-Component Reversible Gray-Scott System on Infinite Lattices by Anhui Gu, Zhaojuan Wang, Shengfan Zhou

“…We prove the existence of a compact random attractor for the random dynamical system generated by stochastic three-component reversible Gray-Scott system with a multiplicative white noise on infinite lattices.…”
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Approximate Solutions for Nash Differential Games by A. A. Megahed, A. A. Hemeda, H. F. A. Madkour

“…The necessary conditions for an open-loop Nash equilibrium solution are obtained, also the existence for the solution of the dynamical system of the differential game is studied. Picard method is used to find an approximate solution, and the uniform convergence is proved. …”
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Asymptotic behavior of solutions for a semibounded nonmonotone evolution equation by Nikos Karachalios, Nikos Stavrakakis, Pavlos Xanthopoulos

“…Also shown is the existence of a global attractor for the corresponding dynamical system.…”
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A Predator-Prey Gompertz Model with Time Delay and Impulsive Perturbations on the Prey by Jianwen Jia, Chunhua Li

“…By using the discrete dynamical system determined by the stroboscopic map, we obtain the sufficient conditions for the existence and global attractivity of the “predator-extinction” periodic solution. …”
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Initial-Sensitive Dynamical Behaviors of a Class of Geometrically Nonlinear Oscillators by Bo Qin, Huilin Shang, Huimin Jiang

“…First, static bifurcation of the dynamical system is discussed. Then, via analyzing the effect of the external excitation on the periodic solutions under primary resonance, it is found that the change of the excitation frequency may lead to bistability and safe jump. …”
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Fractional-Order Sliding Mode Synchronization for Fractional-Order Chaotic Systems by Chenhui Wang

“…The asymptotical stability of the synchronization error dynamical system can be guaranteed by the proposed fractional-order sliding mode controller. …”
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