Kybernetes: Volume 27 Issue 6/7

Introduction: discontinuity – a weakness of calculus and beginning of a new era

In this article, the historical victories and shortfalls of calculus and calculus‐based methods are briefly described so that a need of developing the theory of blown‐ups is…

1. The discontinuity problem and “chaos” of Lorenz’s model

The discontinuity problem of general non‐linear evolutionary equations and the chaos of complex models of poly‐order are studied. The concept of “blown‐up” of Navier‐Stokes…

2. The blown‐up of fluid and two‐phaseness of currents and waves

In this paper, mathematical properties of nonlinearity of the equations in Navier‐Stokes model of currents are studied based on the reasoning logic of systems evolutions, combined…

3. Blown‐ups: a leap from specified local confusions to a general whole evolution

In this paper, we will derive new understandings of some of the problems of mathematics and physics dealt with in the introduction of the concept of blown‐ups and the study of…

4. Modeling of the KdV equation and its solution

Even though the KdV equation can be derived by using either the approximation method of series expansion or the approximation method of harmonics expansion, in the process of…

5. The transformation group of branching solutions of Lorenz’s equations and “chaos”

In this paper, the theory of groups is used in the discussion of the properties of branching solutions of Lorenz’s models with fixed constants. The result shows that the three…

6. Numerical experiment of Lorenz model with direct difference scheme

In this paper, some issues about model formulation and solving methods for the Lorenz’s model are discussed, which also deals with fundamental characteristics of non‐linear…

7. Some problems on “classical chaos”

In the community of “chaos” theory, a phenomenon, appearing in the study of a modified population evolutionary model, i.e. “one‐dimensional iteration”, under certain restrictions…

8. Blown‐ups of laser model and limitations of slaving principle

In this paper, we apply the concept of blown‐ups to discuss the laser evolution model. Our first conclusion implies that: after a certain amount of photons have been absorbed…

9. Discussion on blown‐ups of nonlinear models in chemical reactions

Based on the theory of blown‐ups, in this paper, we will analyze chemical reaction problems, such as the rate of chemical reactions, gaseous chemical reactions, liquid chemical…

10. Blown‐ups of heat‐conduction of ground temperature

In this paper, a class of nonlinear heat‐conduction equations is derived. The properties of these heat‐conduction equations are analyzed. It is shown that the solutions of these…

11. Prediction and analysis of 1994 torrential rains in Southern China

This paper contains an application of the study on shallow water currents. With the employment of the tool of the first and the second lines of defense of the blown‐up graphs, and…

12. Numerical experiments on “stability” of 2‐D quasi‐linear advection equation

While still arguing whether a quasi‐linear equation has a “stability” problem in integration, comparative analyses are made by numerical experimentations using conservation with…

13. Applications of the theory of blown‐ups to weather forecasting

The nonhomogeneous information is applied to the study of sudden and severe weather processes in this paper, based on the theory of blown‐ups (OuYang, 1994). Severe weather…

14. Ground temperature “currents” and earthquake prediction

Based on the theory of blown‐ups, as described by OuYang in 1995 and 1994, for nonlinear dynamic systems on general pansystems transformation, optimization and panderivatives…

15. Nonlinear analysis of population evolution models

Based on the concept of blown‐ups of evolution, introduced by OuYang in 1995, for nonlinear models, the logistic model and its modification of population evolutions are analyzed…

16. Invisible Tao and realistic nonlinearity proposition

In this paper, we consider the fundamental characteristics of motion in the universe in terms of the whole and local evolutionary forms of fluids, based on the theory of blown‐ups…

17. Dialogue on blown‐up theory and some problems in modern evolutionary systems

Blown up theory is very important in modern forecasting science, and will result in revolution not only in forecasting theories but also in applied theories and applied methods…

18. Review and prospects

In this article, a review of the past history of open problems and challenges facing the theory of blown‐ups is given. It expresses the hope that the open problems and challenges…

19. Shoucheng OuYang, where the legend begins

In this paper, a detailed historical account of the birth, development, and applications of the theory of blown‐ups is given.

Preface