41 citations · 164 across the 18 of their papers we have counts for
19 papers
Primes Distribution Linearity. Composite Numbers Cyclicity. Chaoticity of Primes. Twin Primes Occurrence
Marek Berezowski
In this paper it was shown that all prime numbers lie on 96 half-lines. At the same time, it was shown that if a given number does not lie on any of the above half-lines, then it i…
Spectral, entropy and bifurcation analysis of the dynamics of a reverse-flow system
Marek Berezowski, Natalia Kozioł, Marcin Lawnik
The work concerns the spectral, entropy and bifurcation analysis of the dynamics of a reverse-flow system. The existence of chaotic oscillations was demonstrated in a wide range of…
Chaos predictability in a chemical reactor
Marek Berezowski
The dynamics of the tubular chemical reactor with mass recycle were examined. In such a system, temperature and concentrations may oscillate chaotically. This means that state vari…
Chaotic distribution of prime numbers and digits of
Marek Berezowski
In the paper the distribution of prime numbers and digits of were presented as chaotic.
Limit cycles that do not comprise steady states of reactors
Marek Berezowski
It is possible that self-induced oscillations appear in reactors, and that their range does not reach the steady state, although such state exists. To prove this, a cascade of tank…
Predictability of a system with transitional chaos
Marek Berezowski
The paper is focused on the discussion of the phenomenon of transitional chaos in dynamic autonomous and non-autonomous systems. This phenomenon involves the disappearance of chaot…
Homoclinic orbits in a porous pellet
Andrzej Burghardt, Marek Berezowski
The analysis performed as well as extensive numerical simulations have revealed the possibility of the generation of homoclinic orbits as a result of homoclinic bifurcation in a po…
The parametric continuation method for determining steady state diagrams
Marek Berezowski
The paper discusses a simple method of using the parametric continuation method to designate complex diagrams of steady states. The main advantage of the discussed approach is the…
Fractal structure of iterative time profiles
Marek Berezowski, Katarzyna Bizon
The scope of the paper is the theoretical analysis of the time rate in which a dynamical system reaches a stable stationary state or stable oscillations. The method used for the an…
Dynamic of the extended Mandelbrots equation
Marek Berezowski
The paper deals with the mathematical - numerical analysis of the Mandelbrot equation extended by the dynamic continuous term. The possibilities of generation of fractal patterns w…
Fractal trajectories of the dynamical system
Marek Berezowski
The scope of the paper is a theoretical analysis of the dynamical system, the model of which was reduced to Weierstrasse function. A fractal structure of the trajectory was proved…
Periodicity of chaotic solutions
Marek Berezowski, Bozena Kulik
The scope of the paper is the analysis of the impact of flow reversal on the dynamics of cascades of reactors. Periodic and chaotic oscillations occur in the analyzed system. There…
Effect of delay time on the generation of chaos in continuous systems
Marek Berezowski
The present study deals with a theoretical analysis of the effect of delay time of energy transport upon the generation of complex dynamics in continuous physical system. The impor…
Chaotic and non-chaotic mixed oscillations in a logistic systems with delay
Marek Berezowski, Artur Grabski
The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate…
Fractal solutions of reactor models
Marek Berezowski
Three kinds of fractal solutions of model of reactors are presented. The first kind concerns the structure of Feigenbaum_s diagram on the limit of chaos. The second kind and the th…
Bifurcation analysis of the statics and dynamics of a logistic model with two delays
Marek Berezowski, Ewa Fudala
The mathematical - numerical analysis of a discrete dynamical model with two independent delays was performed. Such model may describe a continuous system with delays that have rea…
Bifurcation analysis of the conversion degrees in systems based on the cascade of tank reactors
Marek Berezowski
The scope of the paper is the analysis of the possibility of increasing conversion in different types of systems based on continuous stirred tank reactors. A numerical model of the…
Identification of fast-changing signals by means of adaptive chaotic transformations
Marek Berezowski, Marcin Lawnik
The adaptive approach of strongly non-linear fast-changing signals identification is discussed. The approach is devised by adaptive sampling based on chaotic mapping in yourself of…
Identification of the oscillation period of chemical reactors by chaotic sampling of the conversion degree
Marcin Lawnik, Marek Berezowski
To stabilize the periodic operation of a chemical reactor the oscillation period should be determined precisely in real time. The method discussed in the paper is based on adaptive…