Synchronization of complex dynamical networks with fractional order

Complex dynamical networks (CDN) can be applied to many areas in real world, from medicine, biology, Internet to sociology. Study on CDNs has drawn great attention in recent years. Nodes in a CDN can be modelled as systems represented by differential equations. Study has shown that fractional order differential equations (DF) can better represent some real world systems than integer-order DFs. This research work focuses on synchronization in fractional CDNs.  A literature review on CDNs with fractional order has summarized the latest works in this area.  Fractional chaotic systems are studied in our initial investigation.  Fractional calculus is introduced and the relevant fundamentals to model, describe and analyse dynamical networks are presented. It is shown that the structure and topological characteristics of a network can have a big impact on its synchronizability. Synchronizability and its various interpretations in dynamical networks are studied. To synchronize a CDN efficiently, controllers are generally needed. Controller design is one of the main tasks in this research. Our first design is a new sliding mode control to synchronize a dynamical network with two nodes. Its stability has been proven and verified by simulations.  Its convergence speed outperforms Vaidyanathan's scheme, a well-recognized scheme in this area. The design can be generalized to CDNs with more nodes.  As many applications can be modelled as CDNs with node clustering, a different sliding mode control is designed for cluster synchronization of a CDN with fractional order. Its stability is proven by using Lyapunov method. Its convergence and efficiency is shown in a simulation. Besides these nonlinear methods mentioned, linear control is also studied intensively for the synchronization.  A novel linear method for synchronization of fractional CDNs using a new fractional Proportional-Integral (PI) pinning control is proposed.  Its stability is proven and the synchronization criteria are obtained. The criteria have been simplified using two corollaries so the right value for the variables can be easily assigned. The proposed method is compared with the conventional linear method which uses Proportional (P) controller. In the comparison, the mean squared error function is used. The function measures the average of the squared errors and it is an instant indicator of the synchronization efficiency. A numerical simulation is repeated 100 times to obtain the averages over these runs. Each simulation has different random initial values for both controllers. The average of the errors in all the 100 simulations is obtained and the area under the function curve is defined as an overall performance index (OPI), which indicates the controller's overall performance. In control, small overshoot is always desired. In our work, the error variation is also used as a measure.  The maximum variation from the average of 100 simulations is calculated and compared for both methods. With all the statistical comparisons, it is clear that with the same power consumption, the proposed method outperforms the conventional one and achieves faster and smoother synchronization. Communication constraints exist in most real world CDNs. Communication constraints and their impact on control and synchronization of CDNs with fractional order are investigated in our study. A new adaptive method for synchronizing fractional CDN with disturbance and uncertainty is designed. Its stability is proven and its synchronization criteria are obtained for both fractional CDN with known and unknown parameters. Random disturbance is also included in both cases. Our results show that the new method is efficient in synchronizing CDNs with presence of both disturbance and uncertainty

Dynamical Systems

Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...

Entropy in Image Analysis II

Image analysis is a fundamental task for any application where extracting information from images is required. The analysis requires highly sophisticated numerical and analytical methods, particularly for those applications in medicine, security, and other fields where the results of the processing consist of data of vital importance. This fact is evident from all the articles composing the Special Issue "Entropy in Image Analysis II", in which the authors used widely tested methods to verify their results. In the process of reading the present volume, the reader will appreciate the richness of their methods and applications, in particular for medical imaging and image security, and a remarkable cross-fertilization among the proposed research areas

18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems: Proceedings

Proceedings of the 18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems, which took place in Dresden, Germany, 26 – 28 May 2010.:Welcome Address ........................ Page I Table of Contents ........................ Page III Symposium Committees .............. Page IV Special Thanks ............................. Page V Conference program (incl. page numbers of papers) ................... Page VI Conference papers Invited talks ................................ Page 1 Regular Papers ........................... Page 14 Wednesday, May 26th, 2010 ......... Page 15 Thursday, May 27th, 2010 .......... Page 110 Friday, May 28th, 2010 ............... Page 210 Author index ............................... Page XII

An Initial Framework Assessing the Safety of Complex Systems

Trabajo presentado en la Conference on Complex Systems, celebrada online del 7 al 11 de diciembre de 2020.Atmospheric blocking events, that is large-scale nearly stationary atmospheric pressure patterns, are often associated with extreme weather in the mid-latitudes, such as heat waves and cold spells which have significant consequences on ecosystems, human health and economy. The high impact of blocking events has motivated numerous studies. However, there is not yet a comprehensive theory explaining their onset, maintenance and decay and their numerical prediction remains a challenge. In recent years, a number of studies have successfully employed complex network descriptions of fluid transport to characterize dynamical patterns in geophysical flows. The aim of the current work is to investigate the potential of so called Lagrangian flow networks for the detection and perhaps forecasting of atmospheric blocking events. The network is constructed by associating nodes to regions of the atmosphere and establishing links based on the flux of material between these nodes during a given time interval. One can then use effective tools and metrics developed in the context of graph theory to explore the atmospheric flow properties. In particular, Ser-Giacomi et al. [1] showed how optimal paths in a Lagrangian flow network highlight distinctive circulation patterns associated with atmospheric blocking events. We extend these results by studying the behavior of selected network measures (such as degree, entropy and harmonic closeness centrality)at the onset of and during blocking situations, demonstrating their ability to trace the spatio-temporal characteristics of these events.This research was conducted as part of the CAFE (Climate Advanced Forecasting of sub-seasonal Extremes) Innovative Training Network which has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 813844

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

Mathematical Modeling of Biological Systems

Mathematical modeling is a powerful approach supporting the investigation of open problems in natural sciences, in particular physics, biology and medicine. Applied mathematics allows to translate the available information about real-world phenomena into mathematical objects and concepts. Mathematical models are useful descriptive tools that allow to gather the salient aspects of complex biological systems along with their fundamental governing laws, by elucidating the system behavior in time and space, also evidencing symmetry, or symmetry breaking, in geometry and morphology. Additionally, mathematical models are useful predictive tools able to reliably forecast the future system evolution or its response to specific inputs. More importantly, concerning biomedical systems, such models can even become prescriptive tools, allowing effective, sometimes optimal, intervention strategies for the treatment and control of pathological states to be planned. The application of mathematical physics, nonlinear analysis, systems and control theory to the study of biological and medical systems results in the formulation of new challenging problems for the scientific community. This Special Issue includes innovative contributions of experienced researchers in the field of mathematical modelling applied to biology and medicine