scholarly journals EDSQ Operator on 2DS and Limit Behavior

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 820 ◽  
Author(s):  
Rawad Abdulghafor ◽  
Hamad Almohamedh ◽  
Badr Almutairi ◽  
Sharyar Wani ◽  
Abdullah Alharbi ◽  
...  
Keyword(s):  
Mathematical Models ◽  
Nonlinear Model ◽  
Limit Behavior ◽  
Two Dimensional ◽  
Quadratic Operator ◽  
Dimensional Simplex ◽  
Doubly Stochastic ◽  
Nonlinear Mathematical Models ◽  
Quadratic Stochastic Operators

This paper evaluates the limit behavior for symmetry interactions networks of set points for nonlinear mathematical models. Nonlinear mathematical models are being increasingly applied to most software and engineering machines. That is because the nonlinear mathematical models have proven to be more efficient in processing and producing results. The greatest challenge facing researchers is to build a new nonlinear model that can be applied to different applications. Quadratic stochastic operators (QSO) constitute such a model that has become the focus of interest and is expected to be applicable in many biological and technical applications. In fact, several QSO classes have been investigated based on certain conditions that can also be applied in other applications such as the Extreme Doubly Stochastic Quadratic Operator (EDSQO). This paper studies the behavior limitations of the existing 222 EDSQ operators on two-dimensional simplex (2DS). The created simulation graph shows the limit behavior for each operator. This limit behavior on 2DS can be classified into convergent, periodic, and fixed.

scholarly journals Nonlinear Convergence Algorithm: Structural Properties with Doubly Stochastic Quadratic Operators for Multi-Agent Systems

2018 ◽  
Vol 8 (1) ◽  
pp. 49-61 ◽  
Author(s):  
Rawad Abdulghafor ◽  
Sherzod Turaev ◽  
Akram Zeki ◽  
Adamu Abubaker
Keyword(s):  
Nonlinear Operator ◽  
Stochastic Matrices ◽  
Multi Agent Systems ◽  
Quadratic Operator ◽  
Dimensional Simplex ◽  
Agent Systems ◽  
Doubly Stochastic ◽  
Degroot Model ◽  
Multi Agent ◽  
Time Required

Abstract This paper proposes nonlinear operator of extreme doubly stochastic quadratic operator (EDSQO) for convergence algorithm aimed at solving consensus problem (CP) of discrete-time for multi-agent systems (MAS) on n-dimensional simplex. The first part undertakes systematic review of consensus problems. Convergence was generated via extreme doubly stochastic quadratic operators (EDSQOs) in the other part. However, this work was able to formulate convergence algorithms from doubly stochastic matrices, majorization theory, graph theory and stochastic analysis. We develop two algorithms: 1) the nonlinear algorithm of extreme doubly stochastic quadratic operator (NLAEDSQO) to generate all the convergent EDSQOs and 2) the nonlinear convergence algorithm (NLCA) of EDSQOs to investigate the optimal consensus for MAS. Experimental evaluation on convergent of EDSQOs yielded an optimal consensus for MAS. Comparative analysis with the convergence of EDSQOs and DeGroot model were carried out. The comparison was based on the complexity of operators, number of iterations to converge and the time required for convergences. This research proposed algorithm on convergence which is faster than the DeGroot linear model.

scholarly journals Dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex

2016 ◽  
Vol 14 (1) ◽  
pp. 509-519 ◽  
Author(s):  
Rawad Abdulghafor ◽  
Farruh Shahidi ◽  
Akram Zeki ◽  
Sherzod Turaev
Keyword(s):  
Fixed Points ◽  
Extreme Points ◽  
Initial Point ◽  
Higher Dimensions ◽  
Periodic Points ◽  
Two Dimensional ◽  
Invariant Curves ◽  
Dimensional Simplex ◽  
Doubly Stochastic ◽  
Finite Dimensional

Abstract The present paper focuses on the dynamics of doubly stochastic quadratic operators (d.s.q.o) on a finite-dimensional simplex. We prove that if a d.s.q.o. has no periodic points then the trajectory of any initial point inside the simplex is convergent. We show that if d.s.q.o. is not a permutation then it has no periodic points on the interior of the two dimensional (2D) simplex. We also show that this property fails in higher dimensions. In addition, the paper also discusses the dynamics classifications of extreme points of d.s.q.o. on two dimensional simplex. As such, we provide some examples of d.s.q.o. which has a property that the trajectory of any initial point tends to the center of the simplex. We also provide and example of d.s.q.o. that has infinitely many fixed points and has infinitely many invariant curves. We therefore came-up with a number of evidences. Finally, we classify the dynamics of extreme points of d.s.q.o. on 2D simplex.

scholarly journals Onξ(s)-Quadratic Stochastic Operators on Two-Dimensional Simplex and Their Behavior

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Farrukh Mukhamedov ◽  
Mansoor Saburov ◽  
Izzat Qaralleh
Keyword(s):  
Time Evolution ◽  
General Problem ◽  
Operator Theory ◽  
Nonlinear Operator ◽  
Two Dimensional ◽  
Dimensional Simplex ◽  
Nonlinear Operators ◽  
Quadratic Stochastic Operator ◽  
Stochastic Operator ◽  
Quadratic Stochastic Operators

A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. The general problem in the nonlinear operator theory is to study the behavior of operators. This problem was not fully finished even for quadratic stochastic operators which are the simplest nonlinear operators. To study this problem, several classes of QSO were investigated. We studyξ(s)-QSO defined on 2D simplex. We first classifyξ(s)-QSO into 20 nonconjugate classes. Further, we investigate the dynamics of three classes of such operators.

scholarly journals A Possible Three-Dimensional Mechanism for Oscillating Wobbles in Tropical Cyclone–Like Vortices with Concentric Eyewalls

2018 ◽  
Vol 75 (7) ◽  
pp. 2157-2174 ◽  
Author(s):  
Konstantinos Menelaou ◽  
M. K. Yau ◽  
Tsz-Kin Lai
Keyword(s):  
Tropical Cyclone ◽  
Nonlinear Model ◽  
Three Dimensional ◽  
The Other ◽  
Sensitivity Analyses ◽  
Two Dimensional ◽  
Triggering Mechanism ◽  
Eigenmode Analysis ◽  
Concentric Eyewalls ◽  
Third Dimension

Abstract It is known that concentric eyewalls can influence tropical cyclone (TC) intensity. However, they can also influence TC track. Observations indicate that TCs with concentric eyewalls are often accompanied by wobbling of the inner eyewall, a motion that gives rise to cycloidal tracks. Currently, there is no general consensus of what might constitute the dominant triggering mechanism of these wobbles. In this paper we revisit the fundamentals. The control case constitutes a TC with symmetric concentric eyewalls embedded in a quiescent environment. Two sets of experiments are conducted: one using a two-dimensional nondivergent nonlinear model and the other using a three-dimensional nonlinear model. It is found that when the system is two-dimensional, no wobbling of the inner eyewall is triggered. On the other hand, when the third dimension is introduced, an amplifying wobble is evident. This result contradicts the previous suggestion that wobbles occur only in asymmetric concentric eyewalls. It also contradicts the suggestion that environmental wind shear can be the main trigger. Examination of the dynamics along with complementary linear eigenmode analysis revealed the triggering mechanism to be the excitation of a three-dimensional exponentially growing azimuthal wavenumber-1 instability. This instability is induced by the coupling of two baroclinic vortex Rossby waves across the moat region. Additional sensitivity analyses involving reasonable modifications to vortex shape parameters, perturbation vertical length scale, and Rossby number reveal that this instability can be systematically the most excited. The growth rates are shown to peak for perturbations characterized by realistic vertical length scales, suggesting that this mechanism can be potentially relevant to actual TCs.

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