http://popups.lib.uliege.be/1373-5411/index.php?id=3555 Index terms fr 0 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 http://popups.lib.uliege.be/1373-5411/index.php?id=3551 Most time series analysis is carried out in retrospect, i.e., after the data has been acquired. Direct observation, and with it, anticipation of the temporal development of a system, is often limited to one level of descripion. This would not suffice if one wished to detect scaling behaviour in real time. An algorithm is introduced which describes a fractal, nested detector. This nested detector anticipates scaling structures in real time, and registers space time as a function of the Prime Structure Constant. Depending on where the interfacial cut is set, the nested detector could be a brain, a computer program or a mechanical measuring device. Fractal nested detectors are an example of strong anticipation, as the scaling behaviour, which is inherent in the underlying system's dynamics, is adopted by the detector in order to further differentiate its interface. Tue, 24 Sep 2024 11:48:53 +0200 Tue, 24 Sep 2024 11:49:04 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3551