http://popups.lib.uliege.be/1373-5411/index.php?id=318 Index terms fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=4457 The universal rewrite system, which has previously been applied especially to the generation of the number system and to nilpotent quantum mechanics, not only provides a generalised description for all natural processes but also creates a direct measure of entropy increase and of information transfer, which is especially significant for systems on the edge of chaos. Entropy and information can be shown to have a direct connection with the concept of the generation of the number field at a very fundamental level. Fri, 11 Oct 2024 11:05:08 +0200 Fri, 11 Oct 2024 11:05:28 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=4457 http://popups.lib.uliege.be/1373-5411/index.php?id=4437 This paper deals with a general theory of synchronization of systems coupled by an incursive connection. For systems with a time shift, the slave or driven system anticipates the values of the master or driver system by a future time period giving rise to an anticipatory synchronization. Some extensions show the possibility to enhance the anticipatory synchronization, what we call meta-anticipatory synchronization. An application is shown in the case of an epidemic system represented by a chaotic delayed Pearl-Verhulst map representing the incubation duration of infected susceptibles. A slave model of the infected population is incursively synchronized to the infected population master system, the simulation of which showing that the infected population can be anticipated by a time duration equal to the incubation period. Fri, 11 Oct 2024 09:56:58 +0200 Fri, 11 Oct 2024 09:57:05 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=4437 http://popups.lib.uliege.be/1373-5411/index.php?id=4432 This paper begins with an introduction to the emergence of chaos in a game of evolution proposed recently (Dubois, 1998). The law of conservation of materials in nutrients and populations is used as an environmental closure. Malthusian growth is so transformed to a Pearl-Verhulst map. The game of evolution deals with the competition between a species with its successive mutants. Such a population with random mutations evolves when the ratio birth rateldeath rate of a mutant increases. Chaos appears in such an evolving ecosystem. In this paper, several new basic models of nutrients and population interaction are presented and simulated. Firstly, a second order Pearl-Verhulst is proposed : a second time derivative term is added to the classical Pear-Verhulst model. This term permits to control the velocity of propagation of a population by spatial diffusion. With low value of the diffusion coefficient, the population front is followed by a spatial uniform concentration of the population. For higher values of the diffusion coeflicient bifircations then chaos appear in the spatial structure of the population. This is what we already called a "diffusive chaos" (Dubois, 1996, 1998). Secondly, this second order Pearl-Verhulst can show either the classical chaos either a strange attractor similar to Hénon's attractor (1976). The final states in the bifurcation depends on the initial conditions : this system has a memory of its initial conditions, and the system goes to different attraction basins. Thirdly, the nutrients N - population P interaction model is complicated in adding an intermediate state P* for the population : P* is the satiated population and only non satiated population P can take nutrients. Surprisingly, such an ecosystem has memory but also anticipatory properties similar to the incursive model of the Pearl-Verhulst given before (Dubois, 1996). Such a system depends on the initial conditions and show a strange attractor similar to the Hénon attractor. Fri, 11 Oct 2024 09:44:35 +0200 Fri, 11 Oct 2024 09:44:40 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=4432 http://popups.lib.uliege.be/1373-5411/index.php?id=1026 In this paper is proposed a system to quantify and decrease the effects generated by the chaos factors. To build such a system implies the establishment of some stages, that must be followed very strictly. Each stage is based on some principles, which conduct to the decreasing of risk factors. The authors proposes a lot of principles which allows the building of some scripts that have as objective functions the decreasing of the disturbance's effects generated by the chaos factors. In the paper it is proposed schematic system for quantify and decrease the risk generated by the chaos factors. This system is a multilevel, hierarchical and learning system, in which the commands and adjustments signals are transmitted not continuos but at some periods of times determined by the nature of the system. The system allows the evidence of adjustments loops at each hierarchical level and between the levels. Wed, 03 Jul 2024 16:30:39 +0200 Thu, 10 Oct 2024 16:34:37 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=1026 http://popups.lib.uliege.be/1373-5411/index.php?id=755 The mathematical models for different hierarchical levels of transport processes are discussed. The model equations with memory effects accounting are proposed. Such equations are hyperbolic modifications of the Burgers equation and the Navies- Stokes system. Also the new systems of ordinary differential equations are proposed for investigation memory effects influence on chaos. Some numerical examples of chaotical behaviour in such systems are included. Mon, 01 Jul 2024 10:44:16 +0200 Tue, 08 Oct 2024 14:47:48 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=755 http://popups.lib.uliege.be/1373-5411/index.php?id=2424 This paper deals with the Euler and Incursive algorithms of the nonlinear pendulum. The Euler algorithm is unstable. The incursive algorithms show a stable solution as an orbital stabilify for small values of the time step. For larger values of the time step, the incursive algorithms show an orbital stability for small values of the initial conditions and a chaotic sea for larger initial conditions. Tue, 20 Aug 2024 11:27:28 +0200 Tue, 08 Oct 2024 14:44:03 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2424 http://popups.lib.uliege.be/1373-5411/index.php?id=2605 This paper describes an approach to generate a sequence requiring an unrealizable function by programs, such as a flash that is required especially in creative activity of a human. We have already proposed a recurrent neural network that demonstrates a generation of several creative sequences, but convergency and stability problems occur. On the other hand, it is known in biological experiments where the chaotic sequences can be observed from brain waves. The neural network constructed from chaotic neurons has nonlinear dynamics, but there remains the difficulty of training method. We propose an evolutional methodology to train a chaotic neural network, and introduce Darwinism for its evolving process. To determine their most suitable structure and the weights of connection, we use AIC for the fitness value. Thu, 29 Aug 2024 15:07:30 +0200 Tue, 08 Oct 2024 14:04:11 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2605 http://popups.lib.uliege.be/1373-5411/index.php?id=915 This communication develops the particularities of the"heat-entropy" which are related with the chaotic behaviour of the heat in opposition with the other kinds of energies which are polarized and well directed. By means of a fast survey of every technical domains which are stretched from the Thermodynamic to the Linguistic, including a large range of scientific disciplines related with Systems Theory, we shall discover the usefulness and power of the topic "Entropy" or "Neguentropy" to show the common influence of chaotical seeds in our surrounding. This "entropic" point of view allows a gain for the forecasting. the analysis and the understanding of a lot of events, designs and actions because increase of homogeneity. Neguentropical sight is anavoidably lying in the basement of every teaching _ learning and anticipatitive procedure. Indeed it is always very useful to develop a tool for the highlighting of behavioral analogy between many very various phenomena because it leads to more homogeneous planification in the forecasting procedures and it permits to save much time and a lot of thoughts by their modelings. Mon, 01 Jul 2024 14:07:22 +0200 Mon, 07 Oct 2024 13:53:49 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=915 http://popups.lib.uliege.be/1373-5411/index.php?id=1551 The aim of this paper is to present the author's opinion on the methods used in scientific research whose results are to be applied in practice. It mainly refers to the research whose results describe global problems. This paper's role is also to attract attention to the necessity of system consideration of the anticipation problem (Adamkiewicz, 1997a, 1998b, 1998d, 1998c, 1998e). This view maybe justified on the basis of many sources as well as the author's own research. The process of economic, cultural and social globalization was given as an example of a process in which anticipation plays an essential role (Adamkiewicz, 1995a, 1996, 1997b, 1997e, 1998a, 1999b). Activity anticipating the future should at the same time involve a whole set of such processes. Separate consideration of every process included in the set leads to neglecting the effect of synergy (Adamkiewicz, 1997c, 1997d). At present each particle process is analysed separately applying the non system methods. These methods are in correct (Adamkiewicz, 1989, 1990a, 1990b, 1999c). It is a mistake to use, for example, Maslow's Needs Hierarchy Theory, Pareto's Rule and other methods (Adamkiewicz 1997a, 1999c). The discussed processes take place in arranged social-economic-technical systems. The author postulates the application of proper methods of their analysis. It refers to the theory of chaos due to the non-linear nature of the processes. It also refers to the forecasting methods applied in technical sciences. These methods, based on the theory of change, are the basis of current designing as concept preparation for any social, economic or technical activities. It is also important to draw the attention to the fact that after a period of fascination there is now a backward trend as far as system and cybernetics methods are concerned. Such harmful tendency maybe reversed by arousing interest in the philosophy of the East among certain groups of scientists. This philosophy, on the contrary to the philosophy of the West, is based on system perception of the world. Mon, 15 Jul 2024 14:53:04 +0200 Mon, 07 Oct 2024 12:41:55 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=1551 http://popups.lib.uliege.be/1373-5411/index.php?id=3942 Since the introduction of strong anticipation by D. Dubois the numerous investigations of concrete systems had been proposed. Discrete dynamical systems with anticipation constitute one of such system class. But not very many investigations of such objects exist recently. More intensive investigationso f counterpartst o properties of common systems need- namely to stability of solutions, bifurcation diagrams, chaotic behavior. So the investigation of one modification of well known logistic equation by anticipatory property is considered. One of the most interesting properties in such systems is presumable multivaluednes of the solutions. The next issues are described : the examples of periodic and complex solutions, attractor’s properties, and dependence on the parameters. Tue, 01 Oct 2024 15:51:00 +0200 Tue, 01 Oct 2024 15:51:11 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3942