Paweł Pilarczyk - Profil naukowy - MOST Wiedzy

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Wybrane publikacje

  • Nilpotent singularities and chaos: Tritrophic food chains

    - CHAOS SOLITONS & FRACTALS - Rok 2021

    Local bifurcation theory is used to prove the existence of chaotic dynamics in two well-known models of tritrophic food chains. To the best of our knowledge, the simplest technique to guarantee the emergence of strange attractors in a given family of vector fields consists of finding a 3-dimensional nilpotent singularity of codimension 3 and verifying some generic algebraic conditions. We provide the essential background regarding...

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  • A space-efficient algorithm for computing the minimum cycle mean in a directed graph

    An algorithm is introduced for computing the minimum cycle mean in a strongly connected directed graph with n vertices and m arcs that requires O(n) working space. This is a considerable improvement for sparse graphs in comparison to the classical algorithms that require O(n^2) working space. The time complexity of the algorithm is still O(nm). An implementation in C++ is made publicly available at http://www.pawelpilarczyk.com/cymealg/.

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  • Rigorous numerics for critical orbits in the quadratic family

    - CHAOS - Rok 2020

    We develop algorithms and techniques to compute rigorous bounds for finite pieces of orbits of the critical points, for intervals of parameter values, in the quadratic family of one-dimensional maps fa(x)=a−x2. We illustrate the effectiveness of our approach by constructing a dynamically defined partition P of the parameter interval Ω=[1.4,2] into almost 4 million subintervals, for each of which we compute to high precision the...

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