•A new memristor-based BAM neural network system is formulated.•We analyze the viability and dissipativity of functional differential inclusions’ solutions.•We present a new method to obtain the ...existence of positive periodic solutions.•We utilize the theory of set-valued maps.•The functional differential inclusions of Filippov type are employed.
In this paper, we formulate and investigate a class of memristor-based BAM neural networks with time-varying delays. Under the framework of Filippov solutions, the viability and dissipativity of solutions for functional differential inclusions and memristive BAM neural networks can be guaranteed by the matrix measure approach and generalized Halanay inequalities. Then, a new method involving the application of set-valued version of Krasnoselskii’ fixed point theorem in a cone is successfully employed to derive the existence of the positive periodic solution. The dynamic analysis in this paper utilizes the theory of set-valued maps and functional differential equations with discontinuous right-hand sides of Filippov type. The obtained results extend and improve some previous works on conventional BAM neural networks. Finally, numerical examples are given to demonstrate the theoretical results via computer simulations.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
The field of mathematics has produced many beautiful results, and among them, fixed points hold great importance as they can be used to describe and explain various mathematical curiosities, even ...those of the most complex technical applications. This book explores some of the latest and most fascinating results on the study of fixed points from a scientific perspective and presents new approaches to studying them along with possible applications.
We study relationships between a set-valued map and its inverse limit about the notion of periodic point set, transitivity, sensitivity and Devaney chaos. We show that periodic point set of a ...set-valued map is dense if and only if periodic point set of the inverse limit with the set-valued map is dense. Sensitivity of a set-valued map and its inverse limit are independent of each other. If the inverse limit with the set-valued map is chaotic in the sense of Devaney (respectively, transitive), then the set-valued map is chaotic in the sense of Devaney (respectively, transitive).
•It is a nontrivial generalization from the continuous sel-map and its inverse limit.•Use reverse map, a difficult problem decomposed into several relatively easy ones.•The issues discussed are comprehensive.
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In this work we are concerned with the controllability of first order distributed systems with a general nonlocal condition. Specifically, by a general nonlocal condition we understand a nonlocal ...condition modeled in terms of an inclusion. In this context, assuming that the underlying linear system is approximately controllable, we present three types of conditions under which the nonlinear system is also approximately controllable.
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In this paper, the notion of an original point for a topological space is introduced. Then characterizations of some spaces such as stratifiable spaces and MCP-spaces in terms of set-valued maps with ...values in F(Y), where Y has an original point, are presented.
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This study addresses the problem of quasi-synchronisation of fractional-order memristor-based neural networks (FMNNs) with time delay in the presence of parameter mismatches. Under the framework of ...fractional-order differential inclusions and set-valued maps, quasi-synchronisation of delayed FMNNs is discussed and quasi-synchronisation criteria are established by means of constructing suitable Lyapunov function, together with introducing some fractional-order differential inequalities. A new lemma on the estimate of Mittag–Leffler function is derived first, which extends the application of Mittag–Leffler function and plays a key role in the estimate of synchronisation error bound. Then, linear state feedback combined with delayed state feedback control law is designed, which guarantees that for a predetermined synchronisation error bound, quasi-synchronisation of two FMNNs with mismatched parameters will be achieved provided that the feedback gains satisfy the newly-proposed criteria. The obtained results extend and improve some previous published works on synchronisation of FMNNs. Finally, two numerical examples are given to demonstrate the effectiveness of the obtained results.
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FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
In a capital adequacy framework, risk measures are used to determine the minimal amount of capital that a financial institution has to raise and invest in a portfolio of prespecified eligible assets ...in order to pass a given capital adequacy test. From a capital efficiency perspective, it is important to be able to do so at the lowest possible cost and to identify the corresponding portfolios, or, equivalently, their payoffs. We study the existence and uniqueness of such optimal payoffs as well as their behavior under a perturbation or an approximation of the underlying capital position. This behavior is naturally linked to the continuity properties of the set‐valued map that associates to each capital position the corresponding set of optimal eligible payoffs. Upper continuity can be ensured under fairly natural assumptions. Lower continuity is typically less easy to establish. While it is always satisfied in a polyhedral setting, it generally fails otherwise, even when the reference risk measure is convex. However, lower continuity can often be established for eligible payoffs that are close to being optimal. Besides capital adequacy, our results have a variety of natural applications to pricing, hedging, and capital allocation problems.
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We consider a contact model for a class of generalized materials whose behaviour is described by means of a bipotential. Using the theory of the bipotentials we deliver a weak formulation consisting ...of a system of three variational inequalities. The unknown is a triple having as components the displacement field, the Cauchy stress tensor and a Lagrange multiplier related to the friction force on the frictional contact zone. We investigate the existence of the weak solutions by using a fixed point theorem for set-valued mappings and a minimization technique.
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