Discrete Dynamics in Nature and Society

This paper is devoted to a nonautonomous retarded degenerate parabolic equation. We first show the existence and uniqueness of a weak solution for the equation by using the standard Galerkin method. Then we establish the existence of pullback attractors for the equation by proving the existence of compact pullback absorbing sets and the pullback asymptotic compactness.

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This work introduces a novel modification of classical perturbation method (PM), denominated Optimized Distribution of Boundary Conditions Perturbation Method (ODBCPM) with the purpose to improve the performance of PM in the solution of ordinary differential equations (ODES). We will see that the main proposal of ODBCPM rests above all in the redistribution and optimization of the boundary conditions of the problem to be solved among the iterations of the proposed method. The solution of a couple of heat relevant problems indicates the potentiality of ODBCPM even for the case of large values of the perturbative parameter.

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The framework of outcomes-based education(OBE) has become a central issue for global university education, which is benefited to drive the education development by a series of assessments for historical teaching data, especially student course score, and employment information. The issue of how to timely update the talent training plans for computer major in a university has received considerable critical attention. It is becoming extremely difficult to ignore the requirement of fast shortened update cycle in IT area. One of the main obstacles is that the teaching inertia and the fixed awareness of a major training plan may delay the feedback of teaching problems. There is still a contradiction between the plan rationality and the real-time needs of contemporary IT enterprises. Hence, this paper puts forward a novel data-based framework to evaluate the relevance between the major courses, employment rate, and enterprise needs through the decision tree expression, thus providing reliable data support for systematic curriculum reform. On top of that, A recommendation algorithm is proposed to automatically generate the computer course group that satisfies the staff requirements of IT enterprises. Finally, teaching and employment data of Xihua University in China is applied as an example to undertake course optimization and recommendation. The consequences have an obvious positive effect on student employment and enterprise feedback.

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This paper reports a new bifurcation pattern observed in a Lorenz-type system. The pattern is composed of a main bifurcation route to chaos () and a sequence of sub-bifurcation routes with isolated sub-branches to chaos. When is odd, the isolated sub-branches are from a period- limit cycle, followed by twin period- limit cycles via a pitchfork bifurcation, twin chaotic attractors via period-doubling bifurcations, and a symmetric chaotic attractor via boundary crisis. When is even, the isolated sub-branches are from twin period- limit cycles, which become twin chaotic attractors via period-doubling bifurcations. The paper also shows that the main route and the sub-routes can coexist peacefully by studying basins of attraction.

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The reaction diffusion system is one of the important models to describe the objective world. It is of great guiding importance for people to understand the real world by studying the Turing patterns of the reaction diffusion system changing with the system parameters. Therefore, in this paper, we study Gierer–Meinhardt model of the Depletion type which is a representative model in the reaction diffusion system. Firstly, we investigate the stability of the equilibrium and the Hopf bifurcation of the system. The result shows that equilibrium experiences a Hopf bifurcation in certain conditions and the Hopf bifurcation of this system is supercritical. Then, we analyze the system equation with the diffusion and study the impacts of diffusion coefficients on the stability of equilibrium and the limit cycle of system. Finally, we perform the numerical simulations for the obtained results which show that the Turing patterns are either spot or stripe patterns.

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In this paper, by introducing a convergence comparison property of a self-mapping, we establish some new fixed point theorems for Bianchini type, Reich type, and Dass-Gupta type dualistic contractions defined on a dualistic partial metric space. Our work generalizes and extends some well known fixed point results in the literature. We also provide examples which show the usefulness of these dualistic contractions. As an application of our findings, we demonstrate the existence of the solution of an elliptic boundary value problem.

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