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Conceptualizing Digitalization – What Is a Good Lens to Use?
Published in Sergey V. Samoilenko, Digitalization, 2023
Behavior of a system can be represented in terms of an attractor, which is a set of points in the phase space that defines its steady state motion. Every attractor has a basin of attraction, or a set of points in the space of system variables that evolve to a particular attractor. Aperiodically fluctuating systems said to have a strange attractor. Strange attractors are chaotic when the trajectories in the phase space, from two points very close on the attractor, diverge exponentially due to the system's sensitive dependence on initial conditions and small perturbations in control parameters. The second important insight provided by CT is that while evolutionary path of chaotic system is not predictable, the pattern of the path could be predicted.
The Dynamical Systems Approach to Team Cognition
Published in Michael D. McNeese, Eduardo Salas, Mica R. Endsley, Contemporary Research, 2020
Terri A. Dunbar, Jamie C. Gorman, David A. Grimm, Adam Werner
An attractor is a system state that the system will evolve to regardless of the initial state of the system (Abraham & Shaw, 1992). A repeller, on the other hand, is the opposite—a system state that the system will not approach. Attractors and repellers are either inherently stable (outside disturbances, or perturbations, have little effect), unstable (perturbations have a large effect), or metastable (stability is being actively maintained). The influence of an attractor or repeller is evident from the time course of the system. From the initial system state, the system undergoes a transition period where the system’s behavior fluctuates erratically until it either settles on a behavioral state (i.e., attractor), or settles away from a behavioral state (i.e., repeller). When predicting the future state of the system, a dynamical system will continue to gravitate towards attractors and away from repellers. In teams, attractors have been studied in motor coordination, where the primary interest was attractor formation under certain task constraints (e.g., Gorman & Crites, 2015).
Sine Wave Tracking Is Predictably Attractive
Published in Richard J. Jagacinski, John M. Flach, Control Theory for Humans, 2018
Richard J. Jagacinski, John M. Flach
The formal modeling of this behavior has relied on the concept of an attractor. An attractor is a locus in state space to which a system will return if it is perturbed (e.g., Crutchfield, Farmer, Packard, & Shaw, 1986; Kelso, Ding, & Schoner, 1993). A state space is a space in which the dimensions correspond to a set of variables that, if specified along with any external forces, uniquely determine the future behavior of the system. The two-dimensional phase plane is an example of a state space for simple systems that only require the specification of position and velocity to determine their subsequent behavior. More complicated systems require higher dimensional state spaces to determine their subsequent behavior. The behavior of a system over time forms a trajectory in such a space without any branch points (i.e., the trajectory never acts as though it has reached a fork in the road at which it sometimes turns right and sometimes turns left). If the trajectory did have a branch point, then additional information would be required to determine which branch it would take. However, a state space, by definition, includes sufficient information to avoid such indeterminacy. Therefore, system trajectories in a state space do not exhibit branch points (e.g., Ogata, 1967).
The growth and size of orogenic gold systems: probability and dynamical behaviour
Published in Australian Journal of Earth Sciences, 2023
For any dynamical system, it is important to gain some understanding of the dynamical attractor for that system. The dynamical attractor represents all the thermodynamic states that a system can occupy and the probability density of each state. Thus, it is a representation of all the chemical and physical processes that produced the system. The probability distributions considered earlier in this paper are representative of the density of states that exist on the attractor. This attractor is embedded in a phase space that has, as coordinate axes, the rates of these processes. If there are N independent processes operating, the dimension of phase space is N. For a hydrothermal system N is large and generally of the order of 7–10. It is clearly convenient to reduce the dimensions of the system to 3 so that for visualisation purposes, one can construct a projection of the attractor in N dimensions into three dimensions; an efficient way of doing this is to employ singular value decomposition (SVD). In passing, one should note that the data in a drill hole are a one-dimensional projection of the density of states on the N-dimensional attractor.
Multi-objective trajectory optimization of the 2-redundancy planar feeding manipulator based on pseudo-attractor and radial basis function neural network
Published in Mechanics Based Design of Structures and Machines, 2023
Shenquan Huang, Shunqing Zhou, Luchuan Yu, Jiajia Wang
The steady state of a system is called an attractor. In the practical application, it is difficult for RBFNN algorithm to find the steady state in the complex environment. Under this circumstance, a pseudo-attractor layer in Fig. 3 is introduced based on the attractor theory. The behavior of the pseudo-attractor is similar to that of the real attractor. The pseudo-attractor can pull the learning direction of RBFNN algorithm toward them. It improves the stability and convergence speed of the model. The learning direction of the I-RBFNN algorithm is decided by the updated evaluation criteria in Eq. (16) where Yi is the current learning direction of the I-RBFNN algorithm. is the learning direction of the I-RBFNN algorithm guided by the pseudo-attractor. S is the evaluation criterion. If S is zero, the learning direction will be updated.
Buoyancy-Induced Convection in Water From a Pair of Horizontal Heated Cylinders Enclosed in a Square Cooled Cavity
Published in Heat Transfer Engineering, 2021
Marta Cianfrini, Massimo Corcione, Luca Cretara, Massimo Frullini, Emanuele Habib, Pawel Oclon, Alessandro Quintino, Vincenzo Andrea Spena, Andrea Vallati
Starting from the assigned initial fields of the dependent variables, at each time-step the system of the discretized algebraic governing equations is solved iteratively by the way of a line-by-line application of the Thomas algorithm. A standard under-relaxation technique is enforced in all steps of the computational procedure to ensure an adequate convergence. Within each time-step, the spatial numerical solution of the velocity and temperature fields is considered to be converged when the maximum absolute value of the mass source, as well as the relative changes of the dependent variables at any grid-node between two consecutive iterations, are smaller than the pre-specified values of 10–6 and 10–7, respectively. As time passes, the dynamic behavior of the system is followed by plotting the phase-space trajectories of the dependent variables at some assigned grid nodes, i.e., by plotting the distributions of the local time-derivatives of the dependent variables versus the variables themselves with time as a parameter, whose attractor may be represented by either a fixed point, a limit cycle, a torus, or a so-called strange attractor, in order to visualize the tendency of the system to reach either a steady-state, a periodic, a quasi-periodic, or a chaotic solution. In addition, the time-distributions of the incoming and outgoing heat transfer rates, as well as their relative difference, are continuously monitored to assess the achievement of an asymptotic solution.