Sharif Digital Repository

A complex system consists of a large number of subsystems that interact with each other and with the environment. These systems have collective behaviors that may are desired and undesired. Learning, intelligence and epilepsy are examples of desirable and undesirable collective behaviors. Control of these systems arises when they are out of the desired state or one wants to avoid approaching the system to its undesired state. For control of complex systems, we need external functions that apply to specific subsystems. These functions can be obtained from the numerical solution of Hamilton-Jacobi-Bellman equation. The Hamilton-Jacobi-Bellman equation is nonlinear and must be solved at very... 

In this thesis, we review recent advances on controlling of complex systems. We provide in details, the concepts of synchronizability and synchronization controllability.Then we will investigate synchronization controllability under different pinning schemes, and propose a new pinning strategy to increase controllability and consequently decrease the number of required pinned nodes (known as driver nodes) to assure a stable synchronized state. We also study the network characteristics of resulted sequence of driver nodes. Finally, we will employ our proposed schemes to study the controllability of complex networks of chaotic Rossler oscillators  

In this thesis, we study the resilience of complex systems under structural perturbations. After a brief review of the resilience and its importance, we show that how one can map a system of N-coupled dynamical equations onto an effective one-dimensional dynamics. This procedure is based on a nearest neighbor averaging. The obtained map, helps us study the response of the system to the effective one-dimensional control parameter, instead of all parameters that are affecting the structure of the network. Next, we use this procedure and unveil the resilience pattern of second-order Kuramoto oscillators on complex networks. Moreover, we propose a control strategy for complex systems which is... 

Tipping points occur in diverse systems in various disciplines such as ecology, climate science, economy, sociology, and engineering. Critical thresholds in system parameters or state variables at which a tiny perturbation can lead to a qualitative change in the system exist in many subsystems in complex systems. These thresholds are called tipping points, and these subsystems are called tipping elements. Additionally, many systems with tipping points can be modeled as networks of coupled multistable subsystems. Domino-like tippings are called tipping cascades. Considering that these tipping cascades are primarily unprecedented, it is essential to study the dynamics and control of these... 

A multi-agent system is a system consisting of several intelligent agents. In fact, a multi-agent system is a system that includes a large number of agents that communicate with each other through message transmission in a network structure. Multi-agent systems can solve problems that are difficult or impossible for a single agent or an integrated system to solve. Blockchain is an example of these multi-agent systems that has many use cases in different fields for example cryptocurrencies . A blockchain is a growing ledger consisting of records called blocks. In this thesis, we want to provide tools for the simulation of this multi-agent system so that we can model the issues surrounding... 

These days, self-assembly is one of the most significant phenomena in chemistry and biology. Although There are some Experiments and Simulations which help us to understand self-assembly much more than before, their mechanism is poorly understood. As a result, Calculating Free-energy landscape could be a great development in this area.We use the Flat-histogram monte Carlo algorithm to calculate the density of states of a complex system. In this way, there is a comparison between the exact density of states of Ising Model and the same quantities that are obtained from Flat histogram Method. After that, there would be a combination of statistical thermodynamics and Graph theory toward drawing... 

In this thesis, we have tried to study one of the most well known collective behavior phenomena known as the Wisdom of the crowd, from the perspective of statistical physics. In recent decades with the appearance of Social Networks and mass media, collective social phenomena have become a critical topic in the life of every human being. In the Wisdom of crowd phenomenon, the overall process is to ask the crowd’s opinion regarding a special topic and after aggregating the predicted values, the aggregated quantity is declared as the wisdom of the crowd. It has been observed that in some polls and elections, the result of the wisdom of crowd outperforms every individual of the group and in some... 

Serum osmolality is an important physiological quantity that is directly related to health condition of human body. Glucose, urea, and NaCl are the main components which determine the value of serum osmolality. Besides, calcium and potassium are vital inorganic cations for the body. Thus, it is of high importance to investigate the interactions between these physiological solutes in aqueous solution. Thermodynamic quantities like osmotic and activity coefficients contain enthalpic and entropic information and thus are a direct measure of interactions in these complex systems. Thus, theoretical and experimental methods were applied to investigate these thermodynamic parameters in multi-solute... 

Complex systems involve a large number of degrees of freedom and consist of many components. Interactions of these components with each other, or with an external force, play a significant role in the collective behavior of the complex system.We come across complex systems in many different fields of study including neuroscience, climatology, studying stock markets, etc. The non-linearity of the interactions between their components is what they have in common. Interesting macro-scale properties can be observed in a complex system, as a result of the collective behavior of the system components. We usually focus on studying a group of components in a system, rather than a single component,... 

Multi-vector energy (MVE) networks are one of the most complex systems which are attractive to many researchers. In this work, an integrated gas-power transmission network as an MVE network has been studied. The MVE benchmark used in this work comprises a gas transmission network, which is the core of the MVE, a power transmission network, and a Syn-Gas plant. The gas transmission network supplies the gas demands of its consumers. The main objective of this thesis is to design appropriate controllers to maintain the states of the gas network in its desired condition. Since the gas network is distributed parameter system and its model is an infinite dimensional state space, it is either... 

Complex systems are composed of a large number of subsystems behaving in a collective manner. In such systems, which are usually far from equilibrium, collective behavior arises due to self-organization and results in the formation of temporal, spatial, spatio-temporal and functional structures. The dynamics of order parameters in complex systems are generally non-stationary and can interact with each other in nonlinear manner. As a result, the analysis of the behavior of complex systems must be based on the assessment of the nonlinear interactions, as well as the determination of the characteristics and the strength of the fluctuating forces. This leads to the problem of retrieving a... 

Design of complex systems requires different challenges to be met simultaneously. Yet the current methods lack a sound theoretic framework and thus designers normally rely on heuristic or empirical methods; based on available experiences. Such approaches to the system design entail both technical and business risks and subsequently increase the probability of long-term problems. In this research, along with the theoretical framework of the systems design concepts, we discuss number of important models. The main concentration of the work, however, is to; somehow, correlate Axiomatic Design Matrix (ADM) with Design Structure Matrix (DSM). Here we exploit mathematical model based on sets and by... 

In recent decades, the science of studying complex systems has started to evolve and mature. Complex systems research is becoming ever more important in both the natural and social sciences. The study of mathematical complex system models is used for many scientific questions poorly suited to the traditional mechanistic conception provided by science. Examples of complex systems are Earth's global climate, organisms, the human brain, social organization, an ecosystem, a living cell, and ultimately the entire universe. Motivations for studying complex and self-organized systems can be somewhat divided between science, or attempts to understand such systems, and engineering, or attempts to... 

In this thesis, we first briefly review the basic concepts of stochastic processes. After reviewing and studying the dynamic equation that can explain a stochastic process, we show how one can find on a data-driven basis, the first-, second- and higher-order interactions between different subunits of a complex system by disentangling the dynamics of multivariate time series into stochastic and deterministic parts. Our data-driven approach is to detect different degrees of interactions obtained using conditional moments of Kramers-Moyal coefficients from unconditioned correlation functions and statistical moments of multivariate N-dimensional multivariate time series. Finally, we study the...