Complex Dynamics of a Stochastic Two-Patch Predator-Prey Population Model with Ratio-Dependent Functional Responses by Rong Liu, Guirong Liu

“…First, the existence of a unique global positive solution is proved via the stochastic comparison theorem. Then, two different methods are used to discuss the long-time properties of the solutions pathwise. …”
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On Fixed Points of α-ψ-Contractive Multivalued Mappings in Cone Metric Spaces by Marwan Amin Kutbi, Jamshaid Ahmad, Akbar Azam

“…We obtain some recent results of the literature as corollaries of our main theorem. Moreover, a nontrivial example of α*-ψ-contractive mapping satisfying all conditions of our main result has been constructed.…”
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Common Fixed Points of Intuitionistic Fuzzy Maps for Meir-Keeler Type Contractions by Shazia Kanwal, Akbar Azam

“…The main purpose of this paper is to establish and prove some new common fixed point theorems for intuitionistic fuzzy maps in the context of (α,β)-cut sets of intuitionistic fuzzy sets on a complete metric space in association with the Hausdorff metric. …”
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Existence Results for a Class of p-Laplacian Fractional Differential Equations with Integral Boundary Conditions by SunAe Pak, KumSong Jong, KyuNam O, HuiChol Choi

“…We obtain some existence and uniqueness results concerned with our problem by using Schaefer’s fixed-point theorem and Banach contraction mapping principle. …”
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Finite-Time Pinning Synchronization Control for Coupled Complex Networks with Time-Varying Delays by Hebing Zhang, Xiaojing Zheng, Ning Li

“…Based on the finite-time stability theorem, a finite-time tractive synchronous controller is designed. …”
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Modified Function Projective Synchronization of Financial Hyperchaotic Systems via Adaptive Impulsive Controller with Unknown Parameters by Guoliang Cai, Lingling Zhang, Lan Yao, Xiulei Fang

“…The updated laws of the unknown parameters are given and the sufficient conditions are deduced based on Lyapunov stability theorem and the stability analysis of impulsive system. …”
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Existence and Numerical Simulation of Solutions for Fractional Equations Involving Two Fractional Orders with Nonlocal Boundary Conditions by Jing Zhao, Peifen Lu, Yiliang Liu

“…By means of a fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for the fractional equations. …”
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SEIR epidemiological model with varying infectivity and infinite delay by Gergely Röst, Jianhong Wu

“…Applying a perma-nence theorem for infinite dimensional systems, we obtain that the disease isalways present when $R_0$ > 1.…”
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Duality by reproducing kernels by A. Shlapunov, N. Tarkhanov

“…The matter thus reduces to a regularity theorem for the Neumann problem, a well-known example being the ∂¯-Neumann problem. …”
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Some Bivariate Smooth Compactly Supported Tight Framelets with Three Generators by A. San Antolín, R. A. Zalik

“…Our construction involves some compactly supported refinable functions, the oblique extension principle, and a slight generalization of a theorem of Lai and Stöckler. Estimates for the degrees of smoothness are given. …”
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Approximate Accuracy Approaches to Attribute Reduction for Information Systems by Deshan Liu, Dapeng Wang, Deqin Yan, Yu Sang

“…In order to evaluate the importance of an attribute effectively, a novel algorithm with rigorous theorem is proposed. Experiments show the effect of proposed algorithm.…”
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Novel kernel function for computing the similarity of text by Xiu-hong WANG, Shi-guang JU

“…To enhance the performance of detecting similar documents,a novel kernel function named S_Wang kernel was constructed.Based on the actual situation of computing text similarity,the S_Wang kernel was newly bu lt with consideration of the Euclidean distance and angle between vectors that represented the text documents to be compared.It was proved that the function could be constructed as a kernel function according to Mercer theorem.Experimental verification of the performance of the kernels in the text document similarity calculation was provided.The results show that the S_Wang kernel is significantly better than the precision and F1 performance of other kernels like Cauchy kernel,Latent Semantic Kernel (LSK) and CLA kernel.S_Wang kernel is suitable for text similarity computation.…”
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Normed Ordered and 𝐸-Metric Spaces by Ahmed Al-Rawashdeh, Wasfi Shatanawi, Muna Khandaqji

“…In particular, we get a fixed point theorem of a contractive mapping in 𝐸-metric spaces. …”
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Multiplicity Results to a Conformable Fractional Differential Equations Involving Integral Boundary Condition by Shuman Meng, Yujun Cui

“…Simultaneously, the fixed point theorem for set-valued increasing operator is applied when considering the given problem.…”
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Adaptive Cluster Synchronization for Nondelayed and Delayed Coupling Complex Networks with Nonidentical Nodes by Ze Tang, Jianwen Feng

“…Sufficient conditions are derived to guarantee the realization of the cluster synchronization pattern for all initial values by means of the Lyapunov stability theorem and linear matrix inequalities (LMIs). By using the adaptive update law, relative smaller control gains are obtained, and hence the control cost can be substantially lower. …”
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Algorithms for Solving System of Extended General Variational Inclusions and Fixed Points Problems by Narin Petrot, Javad Balooee

“…By using this equivalent formulation, we prove the existence and uniqueness theorem for solution of the system of extended general nonlinear variational inclusions. …”
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Existence of periodic solutions and homoclinic orbits for third-order nonlinear differential equations by O. Rabiei Motlagh, Z. Afsharnezhad

“…Then we use the Hopf bifurcation theorem for the second-order equation and obtain many periodic solutions for it. …”
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Finite-Time Stability Analysis: A Tutorial Survey by Honglei Xu

“…The finite-time stability analysis in a quantitative sense is reviewed, and a variety of stability results including state transition matrix conditions, the piecewise continuous Lyapunov-like function theory, and the converse Lyapunov-like theorem are investigated. Then, robustness and time delay issues are studied. …”
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Dynamics of a controlled discrete prey-predator model with Holling type-II functional response by Yanlin Min, Xiaoling Han, Ceyu Lei

“…Secondly, we use the central manifold theorem and bifurcation theory to prove that two different types of bifurcations in the system, namely flip bifurcation and Hopf bifurcation. …”
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Existence of positive solutions for generalized quasilinear Schrödinger equations with Sobolev critical growth by Nian Zhang, Chuchu Liang

“…The positive solutions to semilinear equations are then presented using the Mountain Pass Theorem for locally Lipschitz functionals and the Concentration-Compactness Principle. …”
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