Janusz Brzd&#x119;k

Krzysztof Ciepli&#x144;ski

Ajda Fo&#x161;ner

Zbigniew Le&#x15b;niak

Dorian Popa

Bing Xu

Approximate and Iterative Methods

Consideration was given to the discrete optimal control method for the optimal fishing strategy. Our method is new and efficient for discrete optimal control problem, which is different from the other optimal methods such as the traditional variational method, the Pontryagin principle of maximum, and the dynamic programming. The basic construction of the model is the traditional logistic function relating to the growth of fry. The discrete optimal control method for optimal fishing strategy was used to construct the optimal rate of each fishing strategy; the main focus of our work is on the rigorous mathematical analysis of the optimal control problem. The analysis allows one to obtain the optimal initial investment amount of the fry and the optimal size of the total catch. Furthermore, when the initial investment amount of the fry is below or above the optimal value and the intrinsic growth rate of fish <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2129908pt" id="M1" height="9.21094pt" version="1.1" viewBox="-0.0498162 -8.99795 8.62618 9.21094" width="8.62618pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path id="g113-83" d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z"/></g></svg> is too small, we derive that fishing operations should not be started in the last few years to make the overall fishing amount optimal. At last, several typical examples are given to illustrate the obtained results.

Lichun Zhang

Qingdao Huang

Discrete Optimal Control Method Based on the Optimal Strategy of Fishing

This paper investigates stability and asymptotic properties of the error with respect to its nominal version of a nonlinear time-varying perturbed functional differential system subject to point, finite-distributed, and Volterra-type distributed delays associated with linear dynamics together with a class of nonlinear delayed dynamics. The boundedness of the error and its asymptotic convergence to zero are investigated with the results being obtained based on the Hyers-Ulam-Rassias analysis.

M. De la Sen

Hyers-Ulam-Rassias Stability of Functional Differential Systems with Point and Distributed Delays

This paper is concerned with finite-time stabilization (FTS) analysis for a class of uncertain switched positive linear systems with time-varying delays. First, a new definition of finite-time boundedness (FTB) is introduced for switched positive system. This definition can simplify FTS analysis. Taking interval and polytopic uncertainties into account, a robust state feedback controller is built such that the switched positive linear system is finite-time bounded. Finally, an example is employed to illustrate the validities of obtained results.

Tianjian Yu

Yanke Zhong

Tefang Chen

Chunyang Chen

Finite-Time Stabilization of Uncertain Switched Positive Linear Systems with Time-Varying Delays

With the great risk exposed in IT outsourcing, how to assess IT outsourcing risk becomes a critical issue. However, most of approaches to date need to further adapt to the particular complexity of IT outsourcing risk for either falling short in subjective bias, inaccuracy, or efficiency. This paper proposes a dynamic algorithm of risk assessment. It initially forwards extended three layers (risk factors, risks, and risk consequences) of transferring mechanism based on transaction cost theory (TCT) as the framework of risk analysis, which bridges the interconnection of components in three layers with preset transferring probability and impact. Then, it establishes an equation group between risk factors and risk consequences, which assures the &#x201c;attribution&#x201d; more precisely to track the specific sources that lead to certain loss. Namely, in each phase of the outsourcing lifecycle, both the likelihood and the loss of each risk factor and those of each risk are acquired through solving equation group with real data of risk consequences collected. In this &#x201c;reverse&#x201d; way, risk assessment becomes a responsive and interactive process with real data instead of subjective estimation, which improves the accuracy and alleviates bias in risk assessment. The numerical case proves the effectiveness of the algorithm compared with the approach forwarded by other references.

Guodong Cong

Tinggui Chen

A Novel Dynamic Algorithm for IT Outsourcing Risk Assessment Based on Transaction Cost Theory

Animal migration optimization (AMO) is one of the most recently introduced algorithms based on the behavior of animal swarm migration. This paper presents an improved AMO algorithm (IAMO), which significantly improves the original AMO in solving complex optimization problems. Clustering is a popular data analysis and data mining technique and it is used in many fields. The well-known method in solving clustering problems is <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2129898pt" id="M1" height="9.89089pt" version="1.1" viewBox="-0.0498162 -9.6779 6.9399 9.89089" width="6.9399pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path id="g113-108" d="M480 416C480 431 465 448 438 448C388 448 312 383 252 330C217 299 188 273 155 237H153L257 680C262 700 263 712 253 712C240 712 183 684 97 674L92 648L126 647C166 646 172 645 163 606L23 -6L29 -12C51 -5 77 2 107 8C115 62 130 128 142 180C153 193 179 220 204 241C231 170 259 106 288 54C317 0 336 -12 358 -12C381 -12 423 2 477 80L460 100C434 74 408 54 398 54C385 54 374 65 351 107C326 154 282 241 263 299C296 332 351 377 403 377C424 377 436 372 445 368C449 366 456 368 462 375C472 386 480 402 480 416Z"/></g></svg>-means clustering algorithm; however, it highly depends on the initial solution and is easy to fall into local optimum. To improve the defects of the <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2129898pt" id="M2" height="9.89089pt" version="1.1" viewBox="-0.0498162 -9.6779 6.9399 9.89089" width="6.9399pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><use xlink:href="#g113-108"/></g></svg>-means method, this paper used IAMO for the clustering problem and experiment on synthetic and real life data sets. The simulation results show that the algorithm has a better performance than that of the <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2129898pt" id="M3" height="9.89089pt" version="1.1" viewBox="-0.0498162 -9.6779 6.9399 9.89089" width="6.9399pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><use xlink:href="#g113-108"/></g></svg>-means, PSO, CPSO, ABC, CABC, and AMO algorithm for solving the clustering problem.

Mingzhi Ma

Qifang Luo

Yongquan Zhou

Xin Chen

Liangliang Li

An Improved Animal Migration Optimization Algorithm for Clustering Analysis

New sufficient conditions are obtained for oscillation for the solutions of systems of a class of higher-order quasilinear partial functional differential equations with distributed deviating arguments. The obtained results are illustrated by example.

Youjun Liu

Jianwen Zhang

Jurang Yan

Oscillation Properties for Systems of Higher-Order Partial Differential Equations with Distributed Deviating Arguments

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<p><em>Discrete Dynamics in Nature and Society</em> publishes research that links basic and applied research relating to discrete dynamics of complex systems encountered in the natural and social sciences.</p>


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<p>Chief Editor, Dr&nbsp;Renna, is an associate professor at the University of Basilicata, Italy. His research interests include manufacturing systems, production planning and enterprise networks.&nbsp;</p>


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Discrete Dynamics in Nature and Society