查看更多>>摘要：? 2022In this paper, the problem of H∞ resilient filter for nonlinear network systems with dynamic event-triggered mechanism and hybrid cyber attack is discussed. The Takagi-Sugeno (T-S) fuzzy technique is applied to deal with the nonlinearity of network systems. For the obtained T-S fuzzy model, the system measurement output is assumed to transfer to the filter by network channels. A novel dynamic event-triggered communication scheme is proposed to improve the utilization of network resources. In addition, Bernoulli binomial distribution are used to simultaneously describe the phenomenon of deception and DoS attack. Multi-channel network delay is solved by the method of combining delay division and segmented Lyapunov-Krasovskii functional. The co-design conditions of the H∞ resilient filter based on dynamic event-triggered are given by the form of linear matrix inequalities (LMIs), and ensures that the error filtering system is stochastically stable under the H∞ performance index. Finally, the effectiveness and superiority of the filter are verified by the joint simulation of Matlab and Carsim.
查看更多>>摘要：? 2022 Elsevier Inc.In some maps the existence of an attractor with a positive Lyapunov exponent can be proved by constructing a trapping region in phase space and an invariant expanding cone in tangent space. If this approach fails it may be possible to adapt the strategy by considering an induced map (a first return map for a well-chosen subset of phase space). In this paper we show that such a construction can be applied to the two-dimensional border-collision normal form (a continuous piecewise-linear map) if a certain set of conditions are satisfied and develop an algorithm for checking these conditions. The algorithm requires relatively few computations, so it is a more efficient method than, for example, estimating the Lyapunov exponent from a single orbit in terms of speed, numerical accuracy, and rigor. The algorithm is used to prove the existence of an attractor with a positive Lyapunov exponent numerically in an area of parameter space where the map has strong rotational characteristics and the consideration of an induced map is critical for the proof of robust chaos.
查看更多>>摘要：? 2022In this paper, we present a fourth-order difference scheme for solving the Allen-Cahn equation in both 1D and 2D. The proposed scheme is described by the compact difference operators together with the additional stabilized term. As a matter of fact, the Allen-Cahn equation contains the nonlinear reaction term which is eminently proved that numerical schemes are mostly nonlinear. To solve the complexity of nonlinearity, the Crank-Nicolson/Adams-Bashforth method is applied in order to deal with the nonlinear terms with the linear implicit scheme. The well-known energy-decaying property of the equation is maintained by the proposed scheme in the discrete sense. Additionally, the L∞ error analysis is carried out in the 1D case in a rigorous way to show that the method is fourth-order and second-order accuracy for the spatial and temporal step sizes, respectively. Concurrently, we examine the L2 and H1 error analysis for the scheme in the case of 2D. We consider the impact of the additional stabilized term on numerical solutions. The consequences confirm that an appropriate value of the stabilized term yields a significant improvement. Moreover, relevant results are carried out in the numerical simulations to illustrate the faithfulness of the present method by the confirmation of existing pieces of evidence.
查看更多>>摘要：? 2022 Elsevier Inc.In this paper, a suitable state feedback sliding mode controller is designed for the singular fractional order multi-agent systems (SFOMASs) with uncertainty, in order to realize the consensus problem of multi-agent. First, the sliding mode of the designed SFOMAS is in the form of singular systems. The criterion for the admissible consensus of sliding mode is given by using linear matrix inequality (LMI), and an adaptive law based on radial basis function neural network (RBFNN) is established to ensure the accessibility of SFOMASs. Then, a special method is studied to make the sliding mode of the designed SFOMAS normalization. A sufficient condition for the stability and consensus of sliding mode is given by using LMI, and an adaptive law based on RBFNN is established to ensure the accessibility of SFOMAS. Finally, two numerical examples show the applicability of the proposed method.
查看更多>>摘要：? 2022 Elsevier Inc.Recent studies highlight that diffusion processes in highly heterogeneous, fractal-like media can exhibit anomalous transport phenomena, which motivates us to consider the use of generalised transport models based on fractional operators. In this work, we harness the properties of the distributed-order space fractional potential to provide a new perspective on dealing with boundary conditions for nonlocal operators on finite domains. Firstly, we consider a homogeneous space distributed-order model with Beta distribution weight. An a priori estimate based on the L2 norm is presented. Secondly, utilising finite Fourier and Laplace transform techniques, the analytical solution to the model is derived in terms of Kummer's confluent hypergeometric function. Moreover, the finite volume method combined with Jacobi-Gauss quadrature is applied to derive the numerical solution, which demonstrates high accuracy even when the weight function shows near singularity. Finally, a one-dimensional two-layered problem involving the use of the fractional Laplacian operator and space distributed-order operator is developed and the correct form of boundary conditions to impose is analysed. Utilising the idea of ‘geometric reconstruction’, we introduce a ‘transition layer’ whereby the fractional operator index varies from fractional order to integer order across a fine layer at the boundary of the domain when transitioning from the complex internal structure to the external conditions exposed to the medium. An important observation is that for a fractional dominated case, the diffusion behaviour in the main layer is similar to fractional diffusion, while near the boundary the behaviour transitions to the case of classical diffusion.
查看更多>>摘要：? 2022The Lagrangian of a hypergraph is a function that has featured notably in hypergraph Turán densities. Motzkin and Straus established the relationship between Lagrangian and the maximum clique in a graph. As a generalization of Motzkin-Straus Theorem, Frankl and Füredi put forward a well-known conjecture, which states that the r-graph with m edges formed by taking the first m sets in the colex ordering of N(r) has the largest Lagrangian of all r-graphs with m edges. The conjecture was settled when r=3 for sufficiently large m, and is false outside the principal range for r≥4, proved by Gruslys, Letzter and Morrison. Until now, it is still open to characterize the maximisers of the hypergraph Lagrangian outside the principal range for r≥4. In this paper, we study the conjecture outside the principal range. We determine the smallest number of edges for which the conjecture is false, and also partially characterize the maximisers of the Lagrangian.
查看更多>>摘要：? 2022 Elsevier Inc.In this article, we are interested in the fractional discrete p-Laplacian equations on the integers involving different nonlinearities. By employing Clark's theorem and its variants, we prove the multiplicity of homoclinic solutions to the above equations.
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