http://popups.lib.uliege.be/1373-5411/index.php?id=162 Publications of Auteurs Daniel M. Dubois fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=4593 Mon, 14 Oct 2024 14:39:19 +0200 Mon, 14 Oct 2024 14:39:25 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=4593 http://popups.lib.uliege.be/1373-5411/index.php?id=4439 Fri, 11 Oct 2024 10:28:22 +0200 Fri, 11 Oct 2024 10:28:38 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=4439 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=4362 Thu, 10 Oct 2024 10:02:32 +0200 Thu, 10 Oct 2024 10:02:59 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=4362 http://popups.lib.uliege.be/1373-5411/index.php?id=3883 Tue, 01 Oct 2024 09:54:12 +0200 Tue, 01 Oct 2024 09:54:19 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3883 http://popups.lib.uliege.be/1373-5411/index.php?id=3767 Mon, 30 Sep 2024 14:05:34 +0200 Mon, 30 Sep 2024 14:05:42 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3767 http://popups.lib.uliege.be/1373-5411/index.php?id=3667 This paper shows that non-locality property occurs in simple diffusion neural equation: space local incursive discrete equation system transforms to a space non-local recursive equation system. The cable equation used for modelling the potential in neural membrane is similar to the Schrödinger quantum equation with a complex diffusion coefficient. Thu, 26 Sep 2024 10:33:13 +0200 Tue, 08 Oct 2024 14:09:32 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3667 http://popups.lib.uliege.be/1373-5411/index.php?id=3564 Thu, 26 Sep 2024 09:37:03 +0200 Thu, 26 Sep 2024 09:37:14 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3564 http://popups.lib.uliege.be/1373-5411/index.php?id=3351 Mon, 16 Sep 2024 09:55:33 +0200 Mon, 16 Sep 2024 09:55:45 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3351