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Setting the Stage: Complex Systems, Emergence and Evolution
Published in Mariam Kiran, X-Machines for Agent-Based Modeling, 2017
In mathematics, chaos theory is the description of a dynamic system that exhibits high sensitivity to initial conditions of the system. Conversely, chaotic behavior, in common language, also translates into an unpredictable or unperceived behavior. Chaos, thus, has multiple meanings depending in the context it is used. In this book, a chaotic effect refers to an emergent behavior which is unpredictable, or otherwise unknown to observer at the beginning of the simulation. There is a separate research field which involves measuring chaotic points or attractors in a system during simulations, usually measuring initial conditions and then comparing them to a series of outputs generated. Testing these effects of chaos theory is out of the scope of discussions presented here.
InTIME Models and Methods
Published in Susan Krumdieck, Transition Engineering, 2019
This section presents a dynamic model of human systems using feedback control theory (Krumdieck 2014). Feedback control is required for stable operation of any dynamic system, particularly when there are constraints on the inputs, outputs or operating range. How well a system responds to disturbances and to feedback is a measure of the robustness and reliability of the system. Control system theory is a fundamental representation of dynamic system behaviour, which can be applied, in principle, to mechanical, electrical, biological and ecological systems. The concept of feedback control theory is central to the systems thinking used in the InTIME methodology.
Management Theories
Published in W. David Yates, Safety Professional’s, 2015
Chaos theory is a field of study in mathematics, physics, and philosophy studying the behavior of dynamical systems that are highly sensitive to initial conditions. This sensitivity is popularly referred to as the butterfly effect. Small differences in initial conditions yield widely diverging outcomes for chaotic systems, rendering long-term prediction impossible in general. This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved. In other words, the deterministic nature of these systems does not make them predictable.
Optimal control of Hilfer fractional stochastic integrodifferential systems driven by Rosenblatt process and Poisson jumps
Published in Journal of Control and Decision, 2022
K. Ramkumar, K. Ravikumar, E. M. Elsayed
Frequently, the optimal control is largely applied to biomedicine, namely, to model the cancer chemotherapy, and recently applied to epidemiological models and medicine , see Urszula and Schattler (2007) and Ivan et al. (2018) and references therein. The main goal of optimal control is to find, in an open-loop control, the optimal values of the control variables for the dynamic system which maximise or minimise a given performance index. If a fractional differential equation describes the performance index and system dynamics, then an optimal control problem is known as a fractional optimal control problem. Using the fractional variational principle and lagrange multiplier technique, Agrawal (2004) discussed the general formulation and solution scheme for Riemann–Liouville fractional optimal control problems. It is remarkable the fixed point technique, which is used to establish the existence results for abstract fractional differential equations, could be extended to address the fractional optimal control problems. Recently, Aicha et al. (2018) studied the optimal controls of impulsive fractional system with Clarke subdifferential. Very recently, using the LeraySchauder fixed point theorem, Balasubramniam and Tamilalagan (2017) studied the solvability and optimal controls for impulsive fractional stochastic integrodifferential equations. Tamilalagan and Balasubramniam (2018) investigated the solvability and optimal controls for fractional stochastic differential equations driven by Poisson jumps in Hilbert space via analytic resolvent operators and Banach contraction mapping principle.
A graph theory approach for regional controllability of Boolean cellular automata
Published in International Journal of Parallel, Emergent and Distributed Systems, 2020
S. Dridi, S. El Yacoubi, F. Bagnoli, A. Fontaine
Control theory is a branch of mathematics that deals with the behaviour of dynamical systems studied in terms of inputs and outputs. With the recent developments in computing, communications, and sensing technologies, the scope of control theory is rapidly evolving to encompass the increasing complexity of real-life phenomena. Controllability and observability are two major concepts of control theory that have been extensively developed during the last two centuries. The concept of controllability refers to the ability of designing control inputs so as to steer the state of the system to desired values within an interval time while the observability describes whether the internal state variables of the system can be externally measured. These concepts are being increasingly useful in a wide range of applications such as biology, biochemistry, biomedical engineering, ecology, economics, etc. [1,2]. Controllable and observable systems have been characterised so far using the Kalman condition in the linear case. The aim of this paper is to find a general way to give a necessary and sufficient condition for controllability of complex systems via cellular automata models. We concentrate in this work on regional controllability via boundary actions on the target region ω that consists in achieving an objective only in a subdomain of the lattice when some specific actions are exerted on the target region boundaries.
A new chaotic multi-verse optimization algorithm for solving engineering optimization problems
Published in Journal of Experimental & Theoretical Artificial Intelligence, 2018
Gehad Ismail Sayed, Ashraf Darwish, Aboul Ella Hassanien
One of the mathematical approaches that have been employed recently to improve the exploration and exploitation is chaos. Chaos theory is concerned with the study of chaotic dynamical systems that are highly sensitive to initial conditions. Chaos is the phenomenon that occurs in a deterministic nonlinear dynamic system that it is extremely sensitive to the initial condition. It is mathematically defined as a semi-randomness behaviour generated by nonlinear deterministic systems. Therefore, a chaotic movement can travel all states without any repetition within the certain range. Chaotic algorithms have many advantages such as easy implementation and special capacity in order to avoid being trapped in local optima, chaos-based search algorithms have aroused intense interest (Wang, Zheng, & Lin, 2001). In the literature, chaos theory is may be described as the butterfly effect. Therefore, chaotic systems have the properties; namely, sensitivity to primary condition, randomness and deterministic. Using these properties of chaotic systems there are some studies in the literature were proposed for maintaining population diversity and to avoid the local optimum.