Paweł Pilarczyk - Science profile - MOST Wiedzy

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  • Nilpotent singularities and chaos: Tritrophic food chains

    - CHAOS SOLITONS & FRACTALS - 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 - 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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