Open Access
Logistic map neural models
Athanasios Margaris,Manos Roumeliotis +1 more
- 01 Jan 2002
TL;DR: In this paper, the ability of neural-based structures to model the logistic equation was examined, including not only the generative ation of logistic curve, but also the time series that are generated by logistic neural model.
read more
Abstract: This paper examines the ability of neural based structures to model the logistic equation. This modelling includes not only the gener- ation of the logistic curve, but also the time series that are generated by the logistic neural model. This study concerns all main regions of the lo- gistic equation: the region of convergence for parameter values less than 3, the periodic region for parameter values in the interval (3, 3.57), and the chaotic region for values in the interval (3.57, 4). For each region, the flxed points of the logistic map are calculated and compared to the cor- responding theoretical points, followed by an analysis of the distribution of the absolute mean error between the theoretical and the experimental curves. Finally, the Lyapunov exponent and the fractal dimensions for both the theoretical and the neural based attractor are estimated.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Logistic map neural modelling: A theoretical foundation
Athanasios Margaris,Efthimios Kotsialos,Nikos Kofidis,Manos Roumeliotis,Miltiades Adamopoulos +4 more
TL;DR: The attractor paradigm in this paper is the logistic map, which is modelled via neural networks in the convergence, periodic and chaotic regions, and it is proved that, under certain conditions, the function simulated by the neural model is actually theLogistic map with a different value of the λ parameter from the theoretical value.
References
•Book
Chaos: An Introduction to Dynamical Systems
Kathleen T. Alligood,Timothy Sauer,James A. Yorke,J. D. Crawford +3 more
- 07 Nov 1996
TL;DR: One-dimensional maps, two-dimensional map, fractals, and chaotic attraction attractors have been studied in this article for state reconstruction from data, including the state of Washington.
2K
Chaotic time series : Part 1: estimation of some invariant properties in state space
TL;DR: This paper provides a review of two main key features of chaotic systems, the dimensions of their strange attractors and the Lyapunov exponents, and the emphasis is on state space reconstruction techniques that are used to estimate these properties, given scalar observations.
Neural networks: algorithms, applications, and programming techniques
TL;DR: The authors survey the most common neural-network architectures and show how neural networks can be used to solve actual scientific and engineering problems and describe methodologies for simulating neural- network architectures on traditional digital computing systems.
•Book
Adaptive pattern recognition and neural networks
Yoh-Han Pao
- 01 Jan 1989
TL;DR: This is a book that will show you even new to old thing, and when you are really dying of adaptive pattern recognition and neural networks, just pick this book; it will be right for you.