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Search results for: unimodal map
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Uniform expansion estimates in the unimodal map with γ=1.5 as a function of the parameter
Open Research DataThis dataset contains selected results of numerical computations described in the paper "Quantitative hyperbolicity estimates in one-dimensional dynamics" by S. Day, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka, P. Pilarczyk, published in Nonlinearity, Vol. 21, No. 9 (2008), 1967-1987, doi: 10.1088/0951-7715/21/9/002.
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Uniform expansion estimates in the unimodal map with γ=2.5 as a function of the parameter
Open Research DataThis dataset contains selected results of numerical computations described in the paper "Quantitative hyperbolicity estimates in one-dimensional dynamics" by S. Day, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka, P. Pilarczyk, published in Nonlinearity, Vol. 21, No. 9 (2008), 1967-1987, doi: 10.1088/0951-7715/21/9/002.
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Dynamics of S-unimodal maps used in population modeling.
Open Research DataS-unimodal maps are maps of the interval with negative Schwarzian derivative and having only one turning point (such that the map is increasing to the left of the turning point and decreasing to the right of it). Theory of S-unimodal maps is now a well-developed branch of discrete dynamical systems, including famous Singer theorem which implies existence...
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Periodic and chaotic dynamics in a map‐based neuron model
PublicationMap-based neuron models are an important tool in modeling neural dynamics and sometimes can be considered as an alternative to usually computationally costlier models based on continuous or hybrid dynamical systems. However, due to their discrete nature, rigorous mathematical analysis might be challenging. We study a discrete model of neuronal dynamics introduced by Chialvo in 1995. In particular, we show that its reduced one-dimensional...
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Parameter values for topological chaos in the reduced Chialvo model
Open Research DataThe following dataset is connected with a map-based neuron model introduced by D. Chialvo (Chaos, Solitons & Fractals, 5 (3-4) 1995). The reduced version of this model is a one dimensional discrete system which describes the evolution of the membrane voltage when the value of the second variable, the recovery variable, is fixed. We have recently...
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Uniform expansion estimates in the quadratic map as a function of the partition size, using Johnson’s algorithm
Open Research DataThis dataset contains selected results of numerical computations described in the paper "Quantitative hyperbolicity estimates in one-dimensional dynamics" by S. Day, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka, P. Pilarczyk, published in Nonlinearity, Vol. 21, No. 9 (2008), 1967-1987, doi: 10.1088/0951-7715/21/9/002.
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Uniform expansion estimates in the quadratic map with the smallest critical neighborhood for which the expansion exponent λ0 is positive
Open Research DataThis dataset contains selected results of numerical computations described in the paper "Quantitative hyperbolicity estimates in one-dimensional dynamics" by S. Day, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka, P. Pilarczyk, published in Nonlinearity, Vol. 21, No. 9 (2008), 1967-1987, doi: 10.1088/0951-7715/21/9/002.
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Uniform expansion estimates in the quadratic map as a function of the partition size, computing λ only
Open Research DataThis dataset contains selected results of numerical computations described in the paper "Quantitative hyperbolicity estimates in one-dimensional dynamics" by S. Day, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka, P. Pilarczyk, published in Nonlinearity, Vol. 21, No. 9 (2008), 1967-1987, doi: 10.1088/0951-7715/21/9/002.
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Uniform expansion estimates in the quadratic map as a function of the partition size, using the “derivative” partition type
Open Research DataThis dataset contains selected results of numerical computations described in the paper "Quantitative hyperbolicity estimates in one-dimensional dynamics" by S. Day, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka, P. Pilarczyk, published in Nonlinearity, Vol. 21, No. 9 (2008), 1967-1987, doi: 10.1088/0951-7715/21/9/002.
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Uniform expansion estimates in the quadratic map as a function of the parameter, with a large range of parameters
Open Research DataThis dataset contains selected results of numerical computations described in the paper "Quantitative hyperbolicity estimates in one-dimensional dynamics" by S. Day, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka, P. Pilarczyk, published in Nonlinearity, Vol. 21, No. 9 (2008), 1967-1987, doi: 10.1088/0951-7715/21/9/002.
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Uniform expansion estimates in the quadratic map as a function of the parameter, with a very small critical neighborhood
Open Research DataThis dataset contains selected results of numerical computations described in the paper "Quantitative hyperbolicity estimates in one-dimensional dynamics" by S. Day, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka, P. Pilarczyk, published in Nonlinearity, Vol. 21, No. 9 (2008), 1967-1987, doi: 10.1088/0951-7715/21/9/002.
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Uniform expansion estimates in the quadratic map with the smallest critical neighborhood for which the expansion exponent λ is positive
Open Research DataThis dataset contains selected results of numerical computations described in the paper "Quantitative hyperbolicity estimates in one-dimensional dynamics" by S. Day, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka, P. Pilarczyk, published in Nonlinearity, Vol. 21, No. 9 (2008), 1967-1987, doi: 10.1088/0951-7715/21/9/002.
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Uniform expansion estimates in the quadratic map as a function of the critical neighborhood size
Open Research DataThis dataset contains selected results of numerical computations described in the paper "Quantitative hyperbolicity estimates in one-dimensional dynamics" by S. Day, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka, P. Pilarczyk, published in Nonlinearity, Vol. 21, No. 9 (2008), 1967-1987, doi: 10.1088/0951-7715/21/9/002.
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Uniform expansion estimates in the quadratic map as a function of the partition size, using the “critical” partition type
Open Research DataThis dataset contains selected results of numerical computations described in the paper "Quantitative hyperbolicity estimates in one-dimensional dynamics" by S. Day, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka, P. Pilarczyk, published in Nonlinearity, Vol. 21, No. 9 (2008), 1967-1987, doi: 10.1088/0951-7715/21/9/002.
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Uniform expansion estimates in the quadratic map as a function of the parameter, using the “uniform” partition type
Open Research DataThis dataset contains selected results of numerical computations described in the paper "Quantitative hyperbolicity estimates in one-dimensional dynamics" by S. Day, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka, P. Pilarczyk, published in Nonlinearity, Vol. 21, No. 9 (2008), 1967-1987, doi: 10.1088/0951-7715/21/9/002.
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Uniform expansion estimates in the quadratic map as a function of the partition size, using the Floyd–Warshall algorithm
Open Research DataThis dataset contains selected results of numerical computations described in the paper "Quantitative hyperbolicity estimates in one-dimensional dynamics" by S. Day, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka, P. Pilarczyk, published in Nonlinearity, Vol. 21, No. 9 (2008), 1967-1987, doi: 10.1088/0951-7715/21/9/002.
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Uniform expansion estimates in the quadratic map as a function of the parameter, using the “critical” partition type
Open Research DataThis dataset contains selected results of numerical computations described in the paper "Quantitative hyperbolicity estimates in one-dimensional dynamics" by S. Day, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka, P. Pilarczyk, published in Nonlinearity, Vol. 21, No. 9 (2008), 1967-1987, doi: 10.1088/0951-7715/21/9/002.
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Uniform expansion estimates in the quadratic map as a function of the parameter, using the “derivative” partition type
Open Research DataThis dataset contains selected results of numerical computations described in the paper "Quantitative hyperbolicity estimates in one-dimensional dynamics" by S. Day, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka, P. Pilarczyk, published in Nonlinearity, Vol. 21, No. 9 (2008), 1967-1987, doi: 10.1088/0951-7715/21/9/002.
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Uniform expansion estimates in the quadratic map with the smallest critical neighborhood for which the expansion exponent λ0 is greater than 0.1
Open Research DataThis dataset contains selected results of numerical computations described in the paper "Quantitative hyperbolicity estimates in one-dimensional dynamics" by S. Day, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka, P. Pilarczyk, published in Nonlinearity, Vol. 21, No. 9 (2008), 1967-1987, doi: 10.1088/0951-7715/21/9/002.
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Uniform expansion estimates in the quadratic map as a function of the parameter, with a small critical neighborhood
Open Research DataThis dataset contains selected results of numerical computations described in the paper "Quantitative hyperbolicity estimates in one-dimensional dynamics" by S. Day, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka, P. Pilarczyk, published in Nonlinearity, Vol. 21, No. 9 (2008), 1967-1987, doi: 10.1088/0951-7715/21/9/002.
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Uniform expansion estimates in the quadratic map with the smallest critical neighborhood for which the expansion exponent λ is greater than 0.1
Open Research DataThis dataset contains selected results of numerical computations described in the paper "Quantitative hyperbolicity estimates in one-dimensional dynamics" by S. Day, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka, P. Pilarczyk, published in Nonlinearity, Vol. 21, No. 9 (2008), 1967-1987, doi: 10.1088/0951-7715/21/9/002.