13 research outputs found
Multi-weighted complex structure on fractional order coupled neural networks with linear coupling delay: a robust synchronization problem
This sequel is concerned with the analysis of robust synchronization for a multi-weighted complex structure on fractional-order coupled neural networks (MWCFCNNs) with linear coupling delays via state feedback controller. Firstly, by means of fractional order comparison principle, suitable Lyapunov method, Kronecker product technique, some famous inequality techniques about fractional order calculus and the basis of interval parameter method, two improved robust asymptotical synchronization analysis, both algebraic method and LMI method, respectively are established via state feedback controller. Secondly, when the parameter uncertainties are ignored, several synchronization criterion are also given to ensure the global asymptotical synchronization of considered MWCFCNNs. Moreover, two type of special cases for global asymptotical synchronization MWCFCNNs with and without linear coupling delays, respectively are investigated. Ultimately, the accuracy and feasibility of obtained synchronization criteria are supported by the given two numerical computer simulations.This article has been written with the joint financial support of RUSA-Phase 2.0 grant sanctioned vide letter No.F 24-51/2014-U, Policy (TN Multi-Gen), Dept. of Edn. Govt. of India, UGC-SAP (DRS-I) vide letter No.F.510/8/DRSI/2016(SAP-I) and DST (FIST - level I) 657876570 vide letter No.SR/FIST/MS-I/2018/17
Passivity and synchronization of coupled reaction-diffusion complex-valued memristive neural networks
This paper considers two types of coupled reaction-diffusion complex-valued memristive neural networks (CRDCVMNNs). The nodes of the first type CRDCVMNN are coupled through their state and the second one is coupled by spatial diffusion coupling term. For the former, some novel criteria for the passivity and synchronization are derived by constructing an appropriate controller and utilizing some inequality techniques as well as Lyapunov functional method. For the latter, we establish some sufficient conditions which guarantee that this type of CRDCVMNNs can realize passivity and synchronization. Finally, the effectiveness and correctness of the acquired theoretical results are verified by two numerical examples
Nonlinear Systems
Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems
Synchronization of Complex-Valued Dynamical Networks
Dynamical networks (DNs) have been broadly applied to describe natural and human systems consisting of a large number of interactive individuals. Common examples include Internet, food webs, social networks, neural networks, etc. One of the crucial and significant collective behaviors of DNs is known as synchronization. In reality, synchronization phenomena may occur either inside a network or between two or more networks, which are called “inner synchronization” and “outer synchronization”, respectively. On the other hand, many real systems are more suitably characterized by complex-valued dynamical systems, such as quantum systems, complex Lorenz system, and complex-valued neural networks. The main focus of this thesis is on synchronization of complex-valued dynamical networks (CVDNs).
In this thesis, we firstly design a delay-dependent pinning impulsive controller to study synchronization of time-delay CVDNs. By taking advantage of the Lyapunov function in the complex field, some delay-independent synchronization criteria of CVDNs are established, which generalizes some existing synchronization results. Then, by employing the Lyapunov functional in the complex field, several delay-dependent sufficient conditions on synchronization of CVDNs with various sizes of delays are constructed. Moreover, we study synchronization of CVDNs with time-varying delays under distributed impulsive controllers. By taking advantage of time-varying Lyapunov function/ functional in the complex domain, several synchronization criteria for CVDNs with time-varying delays are derived in terms of complex-valued linear matrix inequalities (LMIs). Then, we propose a memory-based event-triggered impulsive control (ETIC) scheme with three levels of events in the complex field to investigate the synchronization problem of CVDNs with both discrete and distributed time delays, and we further consider an event-triggered pinning impulsive control (ETPIC) scheme combining the proposed ETIC and a pinning algorithm to study synchronization of time-delay CVDNs. Results show that the proposed ETIC scheme and ETPIC scheme can effectively synchronize CVDNs with the desired trajectory. Secondly, we study generalized outer synchronization of drive-response time-delayed CVDNs via hybrid control. A hybrid controller is proposed in the complex domain to construct response complex-valued networks. Some generalized outer synchronization criteria for drive-response CVDNs are established, which extend the existing generalized outer synchronization results to the complex field. Thirdly, we study the average-consensus problem of potential complex-valued multi-agent systems. A complex-variable hybrid consensus protocol is proposed, and time delays are taken into account in both the continuous-time protocol and the discrete-time protocol. Delay-dependent sufficient conditions are established to guarantee the proposed complex-variable hybrid consensus protocol can solve the average-consensus problem. Lastly, as a practical application for complex-valued networked systems, the synchronization problem of master-slave complex-valued neural networks (CVNNs) is studied via hybrid control and delayed ETPIC, respectively. We also investigate the state estimation problem of CVNNs by designing the adaptive impulsive observer in the complex field
International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts
The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of
Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the
International Conference on Mathematical Analysis and Applications in Science and Engineering –
ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days).
Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering,
industry, and technology, to discuss the development of new mathematical models, theories, and
applications that contribute to the advancement of scientific knowledge and practice. Authors proposed
research in topics including partial and ordinary differential equations, integer and fractional order
equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization,
control, probability, computational mathematics, amongst others.
The conference was designed to maximize the involvement of all participants and will present the state-of-
the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio