46 citations · 207 across the 21 of their papers we have counts for
22 papers
Systems, environments, and soliton rate equations (II): Toward realistic modeling
Maciej Kuna
In order to solve a system of nonlinear rate equations one can try to use some soliton methods. The procedure involves three steps: (1) Find a `Lax representation' where all the ki…
Simple fractal calculus from fractal arithmetic
Diederik Aerts, Marek Czachor, Maciej Kuna
Non-Newtonian calculus that starts with elementary non-Diophantine arithmetic operations of a Burgin type is applicable to all fractals whose cardinality is continuum. The resultin…
Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus
Diederik Aerts, Marek Czachor, Maciej Kuna
Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration and complex numbers. Applying the formalism to the problem of a Fourier tra…
Crystallization of space: Space-time fractals from fractal arithmetic
Diederik Aerts, Marek Czachor, Maciej Kuna
Fractals such as the Cantor set can be equipped with intrinsic arithmetic operations (addition, subtraction, multiplication, division) that map the fractal into itself. The arithme…
Systems, environments, and soliton rate equations: A non-Kolmogorovian framework for population dynamics
Diederik Aerts, Marek Czachor, Maciej Kuna +1
Soliton rate equations are based on non-Kolmogorovian models of probability and naturally include autocatalytic processes. The formalism is not widely known but has great unexplore…
Quantum Structure in Competing Lizard Communities
Diederik Aerts, Jan Broekaert, Marek Czachor +3
Almost two decades of research on applications of the mathematical formalism of quantum theory as a modeling tool in domains different from the micro-world has given rise to many s…