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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Explicit Wave Solutions and Qualitative Analysis of the (1 + 2)-Dimensional Nonlinear Schrödinger Equation with Dual-Power Law Nonlinearity by Qing Meng, Bin He, Zhenyang Li

“…The (1 + 2)-dimensional nonlinear Schrödinger equation with dual-power law nonlinearity is studied using the factorization technique, bifurcation theory of dynamical system, and phase portraits analysis. From a dynamic point of view, the existence of smooth solitary wave, and kink and antikink waves is proved and all possible explicit parametric representations of these waves are presented.…”
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Analyzing Similarity Solution of Modified Fisher Equation by Esen Hanaç Duruk, Mehmet Emir Koksal, Ram Jiwari

“…The existence of the traveling wave solution to the equation in the long term is observed by using dynamical system theory and exhibiting a phase space analysis of its stable points. …”
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Cosmological Dynamics of a Hybrid Chameleon Scenario by Kourosh Nozari, Narges Rashidi

“…By introducing an effective potential, we study the dependence of the effective potential's minimum and hybrid chameleon field's masses on the local matter density. In a dynamical system technique, we analyze the phase space of this two-field chameleon model, find its fixed points and study their stability. …”
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Basic stage structure measure valued evolutionary game model by John Cleveland

“…A general model of this basic stage structure is formulated as a dynamical system on the state space of finite signed measures.Nonnegativity, well-posedness and uniform eventual boundedness are established under biologically natural conditions on the rates. …”
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Random Dynamics of the Stochastic Boussinesq Equations Driven by Lévy Noises by Jianhua Huang, Yuhong Li, Jinqiao Duan

“…Some fundamental properties of a subordinator Lévy process and the stochastic integral with respect to a Lévy process are discussed, and then the existence, uniqueness, regularity, and the random dynamical system generated by the stochastic Boussinesq equations are established. …”
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New Exact Solutions, Dynamical and Chaotic Behaviors for the Fourth-Order Nonlinear Generalized Boussinesq Water Wave Equation by Cheng Chen, Zuolei Wang

“…Then, the fourth-order nonlinear generalized Boussinesq water wave equation is transformed into the planer dynamical system under traveling wave transformation. We also investigate the dynamical behaviors and chaotic behaviors of the considered equation. …”
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The traveling wave solution and dynamics analysis of the fractional order generalized Pochhammer–Chree equation by Chunyan Liu

“…Second, the dynamic behavior is analyzed using the planar dynamical system, and some three-dimensional and two-dimensional phase portraits are drawn using Maple software to reflect its chaotic behaviors. …”
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Finite-Time Stability Analysis: A Tutorial Survey by Honglei Xu

“…After a brief introduction to notations and two distinct finite-time stability concepts, dynamical system models, particularly in the form of linear time-varying systems and impulsive linear systems, are studied. …”
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Nonlinear Dynamic Analysis and Synchronization of Four-Dimensional Lorenz-Stenflo System and Its Circuit Experimental Implementation by Cheng-Hsiung Yang, Cheng-Lin Wu

“…In this paper, first a new nonlinear chaotic dynamical system had be design, analyze and build circuit. …”
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A multi-base harmonic balance method applied to Hodgkin-Huxley model by Aymen Balti, Valentina Lanza, Moulay Aziz-Alaoui

“…Our aim is to propose a new robust and manageable technique, called multi-base harmonic balance method, to detect and characterize the periodic solutions of a nonlinear dynamical system. Our case test is the Hodgkin-Huxley model, one of the most realistic neuronal models in literature. …”
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Regular and Chaotic Behavior on the Convection in a Rotating Ferrofluid in Porous Medium under Helical Force by M.L. Hounvènou, Vincent Adjimon Monwanou

“…We performed a truncated expansion of Galerkin and found the Lorenz-type model which described the system. The dynamical system is characterized using appropriate and subsequent criteria. …”
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Joint transitivity for linear iterates by Sebastián Donoso, Andreas Koutsogiannis, Wenbo Sun

“…We establish sufficient and necessary conditions for the joint transitivity of linear iterates in a minimal topological dynamical system with commuting transformations. This result provides the first topological analogue of the classical Berend and Bergelson joint ergodicity criterion in measure-preserving systems.…”
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Exact Traveling Wave Solutions and Bifurcation of a Generalized (3+1)-Dimensional Time-Fractional Camassa-Holm-Kadomtsev-Petviashvili Equation by Zhigang Liu, Kelei Zhang, Mengyuan Li

“…Furthermore, the phase portraits of the dynamical system and the remarkable features of the solutions are demonstrated via interesting figures.…”
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Adaptive Synchronization and Antisynchronization of a Hyperchaotic Complex Chen System with Unknown Parameters Based on Passive Control by Xiaobing Zhou, Lianglin Xiong, Weiwei Cai, Xiaomei Cai

“…The essential conditions are derived under which the synchronization or antisynchronization error dynamical system could be equivalent to a passive system and be globally asymptotically stabilized at a zero equilibrium point via smooth state feedback. …”
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A theoretic control approach in signal-controlled metabolic pathways by Ramesh Garimella, Uma Garimella, Weijiu Liu

“…Controllability and observabilityare structural properties of a dynamical system. Thus our resultsmay explain why the metabolic pathways can be controlled andregulated. …”
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Lyapunov Stability in the Cournot Duopoly Game by Dan Zhu, Debing Ni

“…We first explore the relationship between Lyapunov stability at a point, nonsensitivity and non-Devaney chaos and find that a dynamical system is nonsensitive and non-Devaney chaotic if there is a point in this system such that it is Lyapunov stable at that point. …”
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