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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Regularity and Exponential Growth of Pullback Attractors for Semilinear Parabolic Equations Involving the Grushin Operator by Nguyen Dinh Binh

“…We prove the regularity and exponential growth of a pullback attractor in the space S02(Ω)∩L2p−2(Ω) for the nonautonomous dynamical system associated to the problem. The obtained results seem to be optimal and, in particular, improve and extend some recent results on pullback attractors for reaction-diffusion equations in bounded domains.…”
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Chaos Control and Synchronization in Fractional-Order Lorenz-Like System by Sachin Bhalekar

“…The present paper deals with fractional-order version of a dynamical system introduced by Chongxin et al. (2006). …”
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Eigenpairs for the Analysis of Complete Lyapunov Functions by Carlos Argáez, Peter Giesl, Sigurdur Freyr Hafstein

“…A complete Lyapunov function describes the qualitative behaviour of a dynamical system: the areas where the orbital derivative vanishes and where it is strictly negative characterise the chain recurrent set and the gradient-like flow, respectively. …”
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Dynamical Behaviors of a Stage-Structured Predator-Prey Model with Harvesting Effort and Impulsive Diffusion by Lingzhi Huang, Zhichun Yang

“…By the impulsive comparison theorem and the discrete dynamical system determined by the stroboscopic map, we obtain some sufficient conditions on the existence and global attractiveness of predator-eradicated periodic solution for the system. …”
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