Attractor for a Reaction-Diffusion System Modeling Cancer Network by Xueyong Chen, Jianwei Shen, Hongxian Zhou

“…As a result, we establish the existence of the global attractor in L2(Ω)×L2(Ω) and prove that the solution converges to stable steady states. …”
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Coupled flare attractors – a discrete prototype for economic modelling by Georg C. Hartmann, Otto E. Rossler

Subjects: “…Singular-continuous-nowhere-differentiable attractors…”
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Multiple Attractors and Nonlinear Dynamics in an Overlapping Generations Model with Environment by Ahmad Naimzada, Mauro Sodini

“…Relying on numerical and geometrical approaches, various dynamic properties of the proposed model are explored: the existence of the phenomenon of multistability or the coexistence of different attractors was demonstrated. Finally, we describe a nontypical global bifurcation which determines the appearance of an attracting cycle.…”
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Pullback Attractor for Nonautonomous Ginzburg-Landau Equation with Additive Noise by Yangrong Li, Hongyong Cui

“…By making use of Sobolev embeddings and Gialiardo-Nirenberg inequality we obtain the existence and upper semicontinuity of the pullback attractor in L2(I) for the equation. The upper semicontinuity shows the stability of attractors under perturbations.…”
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A bird's eye view to the homeostatic, Alzheimer and Glioblastoma attractors by Joan Nieves, Gabriel Gil, Augusto Gonzalez

“…In addition, reasonable assumptions about the relative strengths of attractors allow to draw a schematic landscape of fitness: a Wright's diagram. …”
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Generalized α-Attractor Models from Elementary Hyperbolic Surfaces by Elena Mirela Babalic, Calin Iuliu Lazaroiu

“…We consider generalized α-attractor models whose scalar potentials are globally well-behaved and whose scalar manifolds are elementary hyperbolic surfaces. …”
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Finite Dimensional Uniform Attractors for the Nonautonomous Camassa-Holm Equations by Delin Wu

“…We consider the uniform attractors for the three-dimensional nonautonomous Camassa-Holm equations in the periodic box Ω=[0,𝐿]3. …”
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Analysis of a New Quadratic 3D Chaotic Attractor by Shahed Vahedi, Mohd Salmi Md Noorani

“…Basic properties of this system show that its corresponding attractor is topologically different from some well-known systems. …”
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Global Attractors in H1(ℝN) for Nonclassical Diffusion Equations by Qiao-zhen Ma, Yong-feng Liu, Fang-hong Zhang

“…We study the existence of global attractors for nonclassical diffusion equations in H1(ℝN). …”
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Pullback Exponential Attractor for Second Order Nonautonomous Lattice System by Shengfan Zhou, Hong Chen, Zhaojuan Wang

“…We first present some sufficient conditions for the existence of a pullback exponential attractor for continuous process on the product space of the weighted spaces of infinite sequences. …”
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The Attractors of the Common Differential Operator Are Determined by Hyperbolic and Lacunary Functions by Wolf Bayer

“…For analytic functions, we investigate the limit behavior of the sequence of their derivatives by means of Taylor series, the attractors are characterized by 𝜔-limit sets. We describe four different classes of functions, with empty, finite, countable, and uncountable attractors. …”
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The Existence of Weak D-Pullback Exponential Attractor for Nonautonomous Dynamical System by Yongjun Li, Xiaona Wei, Yanhong Zhang

“…Then we give a method to obtain the existence of weak D-pullback exponential attractors for a process. As an application, we obtain the existence of weak D-pullback exponential attractor for reaction diffusion equation in H01 with exponential growth of the external force.…”
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Weakly Compact Uniform Attractor for the Nonautonomous Long-Short Wave Equations by Hongyong Cui, Jie Xin, Anran Li

“…Solutions and weakly compact uniform attractor for the nonautonomous long-short wave equations with translation compact forces were studied in a bounded domain. …”
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Global attractor for the lattice dynamical system of a nonlinear Boussinesq equation by Ahmed Y. Abdallah

“…Our objective is to explore the existence of the global attractor for the solution semiflow of the introduced lattice system and to investigate its upper semicontinuity with respect to a sequence of finite-dimensional approximate systems. …”
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Exponential Attractor for a First-Order Dissipative Lattice Dynamical System by Xiaoming Fan

“…And we obtain fractal dimension of the exponential attractor.…”
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Normal Hyperbolicity and Continuity of Global Attractors for a Nonlocal Evolution Equations by Severino Horácio da Silva, Jocirei Dias Ferreira, Flank David Morais Bezerra

“…We show the normal hyperbolicity property for the equilibria of the evolution equation ∂m(r,t)/∂t=-m(r,t)+g(βJ*m(r,t)+βh),  h,β≥0, and using the normal hyperbolicity property we prove the continuity (upper semicontinuity and lower semicontinuity) of the global attractors of the flow generated by this equation, with respect to functional parameter J.…”
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Global Mild Solutions and Attractors for Stochastic Viscous Cahn-Hilliard Equation by Xuewei Ju, Hongli Wang, Desheng Li, Jinqiao Duan

“…Then, we show that the existence of a stochastic global attractor which pullback attracts each bounded set in appropriate phase spaces.…”
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Time-Dependent Global Attractor for a Class of Nonclassical Parabolic Equations by Fang-hong Zhang

“…Based on the recent theory of time-dependent global attractors in the works of Conti et al. (2013) and di Plinio et al. (2011), we prove the existence of time-dependent global attractors as well as the regularity of the time-dependent global attractor for a class of nonclassical parabolic equations.…”
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Initial Value Determination of Chua System with Hidden Attractors and Its DSP Implementation by Xianming Wu, Weijie Tan, Huihai Wang

“…In this paper, a method for determining the initial value of the hidden attractors in the Chua system is studied. The initial value of the hidden attractors can be calculated quickly and accurately by the proposed method, and the hidden attractors can be found by numerical simulation. …”
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Attractor and Vector Structure Analyses of Bursting Oscillation with Sliding Bifurcation in Filippov Systems by Rui Qu, Shaolong Li

“…The attractor analysis proposed in our previous work is used to discuss the complicated oscillations of the Filippov system. …”
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