Theory Of Dissipative Systems Research Articles

Spatial and temporal dynamics of COVID-19 with nonlocal dispersal in heterogeneous environment: Modeling, analysis and simulation

This paper proposes an infectious disease dynamics model with spatial heterogeneity to study the joint impact of nonlocal dispersal and vaccine on the transmission dynamics of COVID-19 (Corona Virus Disease 2019). Overcoming the difficulty of non-compactness caused by non-local operators, the functional expression of the next generation operator R is obtained by using the renewal equation. And then, the basic reproduction number R0 of the proposed model is obtained, i.e., the spectral radius of the next generation operator R. In terms of theoretical analysis, we prove that the global asymptotic stability of the disease-free steady state when R0<1; Using the uniform persistence theory of point dissipative systems, we prove the system is uniformly persistent and has at least one positive steady state when R0>1. We verify the theoretical results and study the influence of related factors on the transmission of COVID-19 pandemic in numerical simulation part. Finally, our numerical results show that: (1) Improving the coverage rate of COVID-19 complete vaccine and the vaccine efficiency is one of the optimal measures to effectively prevent and control the spread of COVID-19 under the current medical conditions; (2) The influence of the form of nonlocal dispersal kernel function and the virus in environment on the transmission of COVID-19 cannot be ignored Therefore, targeted prevention and control measures should be taken for the dispersal of the virus in urban areas and in the process of cold chain transportation to prevent COVID-19 from spreading to rural areas with relatively backward medical conditions.

Weather pattern dynamics over western Europe under climate change: predictability, information entropy and production

Abstract. The impact of climate change on weather pattern dynamics over the North Atlantic is explored through the lens of the information theory of forced dissipative dynamical systems. The predictability problem is first tackled by investigating the evolution of block entropies on observational time series of weather patterns produced by the Met Office, which reveals that predictability is increasing as a function of time in the observations during the 19th century and beginning of the 20th century, while the trend is reversed at the end of the 20th century and beginning of the 21st century. This feature is also investigated in the 15-member ensemble of the UK Met Office CMIP5 model for the 20th and 21st centuries under two climate change scenarios, revealing a wide range of possible evolutions depending on the realization considered, with an overall decrease in predictability in the 21st century for both scenarios. Lower bounds of the information entropy production are also extracted, providing information on the degree of time asymmetry and irreversibility of the dynamics. The analysis of the UK Met Office model runs suggests that the information entropy production will increase by the end of the 21st century, by a factor of 10 % in the Representative Carbon Pathway RCP2.6 scenario and a factor of 30 %–40 % in the RCP8.5 one, as compared to the beginning of the 20th century. This allows one to make the conjecture that the degree of irreversibility is increasing, and hence heat production and dissipation will also increase under climate change, corroborating earlier findings based on the analysis of the thermodynamic entropy production.

DIASPORA CULTURE: THE MAIN METHODOLOGICAL AND TERMINOLOGICAL ASPECTS OF CULTURE LOGICAL COMPREHENSION

The purpose of this article is to justify the necessary of the complex approach to study of the diasporian culture. It is shows that the culture of diaspora usually don`t considered as the original autonomous phenomenon, but only as a small separate marginal part of the native culture. This point of view bases on the outdated ansystem inefficient paradigm of so-called "Island" anthropology. One of the most effective approaches to understanding the essence of culture is theory of dissipative systems. The fact that the theory of dissipative systems not only explains but also proves the naturalness and regularity of the appearance of various branches/ directions of any culture is one of its most important results. Study of the diaspora culture that has been existed during the centuries in another country, it should include research on the entire material sphere of its life, all the artifacts created by its representatives. It is proves the expedience to use iconological method, the approaches of the Actor-Network theory (ANT) and the “Philosophy from below” in this contex. The ANT considers artifacts as active units/ actors of social relations, which make up “sociality”, as well as the principles of "Philosophy from below".

Introduction to Jan C. Willems’, “Dissipative Dynamical Systems, Part II: Linear Systems With Quadratic Supply Rates”

The two-part article, “Dissipative Dynamical Systems,” by Jan C. Willems, was submitted in January 1972 to the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Archive for Rational Mechanics and Analysis</i> and published in the same year (vol. 45, Part I, pp. 321–351, Part II: pp. 352–393). While Part I develops the theory of dissipative systems for general input–state–output systems, Part II confines itself to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">linear systems</i> . Moreover, most of Part II is about dissipativity with respect to the supply rate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$y{\hspace{0.06em}}^{\top}u,$</tex-math></inline-formula> that is, linear <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">passive</i> systems. The main questions addressed in Part II concern the analysis of the set of storage functions of linear passive systems (with the existence of a minimal and maximal element already established in Part I) and the compatibility of storage functions with other external and internal symmetry properties of the system, such as reciprocity and reversibility. (See “The Articles of This Special Issue.”) This links the article closely to the realization theory of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">physical</i> linear systems, in particular, the network synthesis of electrical circuits, the Onsager–Casimir relation of linear thermodynamics, and the input–output analysis of linear viscoelastic systems.

Interconnection and Approximation in Networks of Dissipative Systems: Addressing Topological Simplification

Half a century ago, and a few years after receiving his Ph.D. degree in electrical engineering at the Massachusetts Institute of Technology, Jan Willems published articles on dissipative dynamical systems <xref ref-type="bibr" rid="ref30" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[30]</xref> , <xref ref-type="bibr" rid="ref31" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[31]</xref> . In retrospect, the conceptual thinking and elegant generalization of the basic physical properties behind the notion of dissipation can be viewed as a distinctive stage in the field of systems and control. These articles have sparked an impressive number of scientific and technological contributions in the field of systems theory, mathematical modeling, and control systems synthesis. Especially with the introduction of powerful numerical tools to solve matrix inequalities, the classical theory of dissipative systems has proved a strong, rich, and (above all) elegant conceptual and theoretical framework to solve a plethora of relevant problems in robust control, stabilization, and estimation. It is a pleasure to contribute to a volume on dissipative dynamical systems, 50 years after the publication of these seminal articles.

Make me dictator and I will save humankind

Aim: Humankind finds itself in a dire situation. Solutions have been put forth, but none has made a significant impact on carbon release or resources depletion. I add my proposal, the literary device of the dictator, to those who feel there is some possible remedy for our predicament.&#x0D; Design / Research methods: This paper is part of a larger project which uses micro- and macro-sociology and cliodynamics, archaeology, evolutionary biology, and dissipative systems theory to describe both our global system, and its implications for our species. I briefly critique three other approaches regarding their likelihood of success.&#x0D; Conclusions / findings: The self-organized dissipative system drives population, population density, and the exploitation and depletion of natural resources. The system is the interface between humans and the environment. It is unlikely any approach which is not 1. dramatic, 2. inclusive, and 3. determinedly focused on disarming the global system will prevent the complete depletion of the natural world, and the continued mass extinction.&#x0D; Originality / value of the article: The paper challenges commonly held assumptions regarding the system and human participation in it. The paper should be of interest to anyone concerned about humankind. &#x0D; Implications of the research (if applicable): The paper has strong implications for policy. It describes how perpetuating ideas like “sustainable growth” can only ensure the collapse of the global system, and perhaps the collapse of the natural systems as well. The consequence of applying the research would be desperate, frighteningly objective, but will allow, perhaps, Homo to continue. &#x0D; Limitations of the research (if applicable): Future research could focus on re-interpreting data gathered by previous paradigms. Cliodynamics provides insight into the future by considering complex relationships. The limitations to the implications of the research lie in the fact that it is difficult for some to distinguish between “humankind” and the system.&#x0D;

Robust Stabilization of Inverter-Based Resources Using Virtual Resistance-Based Control

This paper proposes a virtual resistance-based nonlinear control to stabilize and robustify the current layer of inverter-based resources, subject to the grid voltage disturbances, and the grid parameter uncertainties. A class of virtual resistances is proposed and analyzed using concepts from dissipative systems theory. Moreover, specific nonlinear virtual resistance-based controllers are derived, with their corresponding performance analytically bounded. The theoretical and simulation results show that the proposed nonlinear virtual resistance-based controllers significantly reduce the L2 gain of the closed-loop error system to grid voltage variation and parametric uncertainties. Significant improvements of the transient and steady-state current responses are also demonstrated over linear virtual resistance counterparts.

Dynamical conditions and causal transport of dissipative spherical collapse in f(R, T) gravity

In this paper, we have investigated the non-adiabatic spherical gravitational collapse in the framework of the $f(R,T)$ theory of gravity with a locally anisotropic fluid that undergoes dissipation in the form of heat flux, free-streaming radiation, and shearing viscosity. The dynamical equations are analyzed in detail, both in the Newtonian and post-Newtonian regimes. Finally we couple the dynamical equations to the full causal transport equation in the context of Israel-Stewart theory of dissipative systems. This yields us a better understanding of the collapse dynamics and may be connected to various astrophysical consequences.

Robust nonlinear observer design based on impulsive dissipativity

The paper considers the design of a nonlinear dissipative impulsive observer based on non-periodic discrete-time measurements. Sufficient conditions are derived for (i) exponential convergence of the observer in absence of measurement uncertainty, and (ii) input-to-state stability (ISS) with respect to measurement uncertainty, by combining notions from impulsive and dissipative systems theory. The conditions mainly include constraints on the minimum and maximum time between measurements depending on system characteristics, the correction gain and the desired ISS gain. The results are illustrated with a numerical case example.

Stability and dynamic transition of a toxin-producing phytoplankton-zooplankton model with additional food

<p style='text-indent:20px;'>The article aims to investigate the dynamic transitions of a toxin-producing phytoplankton zooplankton model with additional food in a 2D-rectangular domain. The investigation is based on the dynamic transition theory for dissipative dynamical systems. Firstly, we verify the principle of exchange of stability by analysing the corresponding linear eigenvalue problem. Secondly, by using the technique of center manifold reduction, we determine the types of transitions. Our results imply that the model may bifurcate two new steady state solutions, which are either attractors or saddle points. In addition, the model may also bifurcate a new periodic solution as the control parameter passes critical value. Finally, some numerical results are given to illustrate our conclusions.

Quantum theory of dissipative topological systems

Topological phases of matter are protected from local perturbations and therefore have been thought to be robust against decoherence. However, it has not been systematically explored whether and how topological states are dynamically robust against the environment-induced decoherence. In this Letter, we develop a theory for topological systems that incorporate dissipations, noises and thermal effects. We derive novelly the exact master equation and the transient quantum transport for the study of dissipative topological systems, mainly focusing on noninteracting topological insulators and topological superconductors. The resulting exact master equation and the transient transport current are also applicable for the systems initially entangled with environments. We apply the theory to the topological Haldane model (Chern insulator) and the quantized Majorana conductance to explore topological phases of matter that incorporate dissipations, noises and thermal effects, and demonstrate the dissipative dynamics of topological states.

Field theory of dissipative systems with gapped momentum states

We develop a field theory with dissipation based on a finite range of wave propagation and associated gapped momentum states in the wave spectrum. We analyze the properties of the Lagrangian and the Hamiltonian with two scalar fields in different representations and show how the new properties of the two-field Lagrangian are related to Keldysh-Schwinger formalism. The proposed theory is non-Hermitian, and we discuss its properties related to $\mathcal{PT}$ symmetry. The calculated correlation functions show a decaying oscillatory behavior related to gapped momentum states. We corroborate this result using path integration. The interaction potential becomes short-ranged due to dissipation. Finally, we observe that the proposed field theory represents a departure from the harmonic paradigm and discuss the implications of our theory for the Lagrangian formulation of hydrodynamics.

Joint controller and detector design against data injection attacks on actuators

This paper addresses the issue of data injection attacks on actuators in control systems. Considering attacks that aim at maximizing impact while remaining undetected, the paper revisits the recently proposed output-to-output gain, which is compared to classical sensitivity metrics such as H∞ and H-. In its original formulation, the output-to-output gain is unbounded for strictly proper systems. This limitation is further investigated and addressed by modifying the performance output of the system and ensuring that the system from attack signal to performance output is also strictly proper. With this system description, and by using the theory of dissipative systems, a Bi-linear Matrix Inequality (BMI) is formulated for system design. Using this BMI, a design algorithm is proposed based on the heuristic of alternating minimization. Through numerical simulations of the proposed algorithm, it is found that the output-to-output gain presents advantages over the other metrics: the effect of the attack is reduced in the performance output and increased in the detection output in a relatively large spectrum of frequencies.

Dissipativity-Guaranteed Distributed Model Predictive Controller for Reconfigurable Large-Scale System

This paper presents a distributed model predictive control strategy for reconfigurable large-scale systems to maintain global stability when there are subsystems joining in or leaving the system during closed-loop operation, which is also called the plug-and-play control. Dissipativity is an input–output property, and the overall dissipativity property of a large-scale system can be described by the ‘linear’ combination of the dissipativity properties of its subsystems based on their interconnection topology. The capacity of capturing interaction effects among subsystems on overall stability makes dissipative system theory a useful tool to design control system for reconfigurable large-scale system. The redesign is restricted to subsystems whose input–output property will be directly influenced by the topology change in order to allow quick operation. The overall stability condition can still be guaranteed if the dissipativity property of the redesigned subsystems does not spoil the overall dissipativity condition. Simulation results of a power network system with subsystems joining in and leaving the network show the effectiveness of the proposed strategy.

Stability analysis by dynamic dissipation inequalities: On merging frequency-domain techniques with time-domain conditions

This paper provides a complete link between dissipative systems theory and a celebrated result on stability analysis with integral quadratic constraints (IQCs). This is achieved with a new stability characterization for feedback interconnections based on the notion of finite-horizon integral quadratic constraints with a terminal cost. As the main benefit, this opens up opportunities for guaranteeing constraints on the transient responses of trajectories in feedback loops within absolute stability theory. For systems affected by parametric uncertainties, we show how to generate tight robustly invariant ellipsoids on the basis of a classical frequency-domain stability test, with illustrations by a numerical example.

Dynamical transitions of a low-dimensional model for Rayleigh–Bénard convection under a vertical magnetic field

In this article, we study the dynamic transitions of a low-dimensional dynamical system for the Rayleigh–Bénard convection subject to a vertically applied magnetic field. Our analysis follows the dynamical phase transition theory for dissipative dynamical systems based on the principle of exchange of stability and the center manifold reduction. We find that, as the Rayleigh number increases, the system undergoes two successive transitions: the first one is a well-known pitchfork bifurcation, whereas the second one is structurally more complex and can be of different type depending on the system parameters. More precisely, for large magnetic field, the second transition is of continuous type and gives to a stable limit cycle; on the other hand, for low magnetic field or small height-to-width aspect ratio, a jump transition occurs where an unstable periodic orbit eventually collides with the stable steady state, leading to the loss of stability at the critical Rayleigh number. Finally, numerical results are presented to corroborate the analytic predictions.

Dissipation Effects in Schrödinger and Quantal Density Functional Theories of Electrons in an Electromagnetic Field

Dissipative effects arise in an electronic system when it interacts with a time-dependent environment. Here, the Schrödinger theory of electrons in an electromagnetic field including dissipative effects is described from a new perspective. Dissipation is accounted for via the effective Hamiltonian approach in which the electron mass is time-dependent. The perspective is that of the individual electron: the corresponding equation of motion for the electron or time-dependent differential virial theorem—the ‘Quantal Newtonian’ second law—is derived. According to the law, each electron experiences an external field comprised of a binding electric field, the Lorentz field, and the electromagnetic field. In addition, there is an internal field whose components are representative of electron correlations due to the Pauli exclusion principle and Coulomb repulsion, kinetic effects, and density. There is also an internal contribution due to the magnetic field. The response of the electron is governed by the current density field in which a damping coefficient appears. The law leads to further insights into Schrödinger theory, and in particular the intrinsic self-consistent nature of the Schrödinger equation. It is proved that in the presence of dissipative effects, the basic variables (gauge-invariant properties, knowledge of which determines the Hamiltonian) are the density and physical current density. Finally, a local effective potential theory of dissipative systems—quantal density functional theory (QDFT)—is developed. This constitutes the mapping from the interacting dissipative electronic system to one of noninteracting fermions possessing the same dissipation and basic variables. Attributes of QDFT are the separation of the electron correlations due to the Pauli exclusion principle and Coulomb repulsion, and the determination of the correlation contributions to the kinetic energy. Hence, Schrödinger theory in conjunction with QDFT leads to additional insights into the dissipative system.

L2-Gain and Passivity Techniques in Nonlinear Control, Third Edition [Bookshelf

The analysis and control of nonlinear systems is still an important and active area of research. This book, in its third edition, has not strayed from the roots of earlier editions. The text still provides a comprehensive presentation of L2-gain and passivity theory from both the input–output and state-space viewpoints, connected through the dissipative systems framework. Additionally, this book is still a prime reference for energy shaping, nonlinear passivation via state feedback, nonlinear factorizations, and nonlinear H∞ control. However, this new edition includes various rewritten chapters as well as the addition of new material. Specifically, the chapter on dissipative systems in the second edition is now three separate chapters on dissipative systems theory, passive state-space systems, and L2-gain theory. The chapter on port-Hamiltonian systems (PHSs) in the second edition was split into two chapters on PHS theory (Chapter 6) and control of PHSs. The third edition has 11 chapters, compared to eight chapters in the second edition. A summary of each chapter is given next. The book is an excellent reference for both students and researchers. The expansion of the text in the forms of Chapters 3, 4, and 6–8 makes the material more complete and accessible. This text is sure to continue to be one of the go-to references for nonlinear control researchers and practitioners interested in both the classical and modern interpretations and applications of L2-gain and passivity methods for nonlinear systems.

Perturbed cooperative-state feedback strategy for model predictive networked control of interconnected systems

A perturbed cooperative-state feedback (PSF) strategy is presented for the control of interconnected systems in this paper. The subsystems of an interconnected system can exchange data via the communication network that has multiple connection topologies. The PSF strategy can resolve both issues, the sensor data losses and the communication network breaks, thanks to the two components of the control including a cooperative-state feedback and a perturbation variable, e.g., ui=Kijxj+wi. The PSF is implemented in a decentralized model predictive control scheme with a stability constraint and a non-monotonic storage function (ΔV(x(k))≥0), derived from the dissipative systems theory. Numerical simulation for the automatic generation control problem in power systems is studied to illustrate the effectiveness of the presented PSF strategy.

Signatures of classical structures in the leading eigenstates of quantum dissipative systems.

By analyzing a paradigmatic example of the theory of dissipative systems-the classical and quantum dissipative standard map-we are able to explain the main features of the decay to the quantum equilibrium state. The classical isoperiodic stable structures typically present in the parameter space of these kinds of systems play a fundamental role. In fact, we have found that the period of stable structures that are near in this space determines the phase of the leading eigenstates of the corresponding quantum superoperator. Moreover, the eigenvectors show a strong localization on the corresponding periodic orbits (limit cycles). We show that this sort of scarring phenomenon (an established property of Hamiltonian and projectively open systems) is present in the dissipative case and it is of extreme simplicity.