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Effortless estimation of basins of attraction [PDF]
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2022 We present a fully automated method that identifies attractors and their basins of attraction without approximations of the dynamics. The method works by defining a finite state machine on top of the dynamical system flow. The input to the method is a dynamical system evolution rule and a grid that partitions the state space.
George Datseris, Alexandre Wagemakers
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Invited paper: A Review of Thresheld Convergence
GECONTEC: Revista Internacional de Gestión del Conocimiento y la Tecnología, 2022 A multi-modal search space can be defined as having multiple attraction basins – each basin has a single local optimum which is reached from all points in that basin when greedy local search is used. Optimization in multi-modal search spaces can then be
Stephen Chen +3 more
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A Characterization of the Dynamics of Schröder’s Method for Polynomials with Two Roots
Fractal and Fractional, 2021 The purpose of this work is to give a first approach to the dynamical behavior of Schröder’s method, a well-known iterative process for solving nonlinear equations. In this context, we consider equations defined in the complex plane. By using topological
Víctor Galilea, José M. Gutiérrez
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Invited paper: A Review of Thresheld Convergence [PDF]
GECONTEC: Revista Internacional de Gestión del Conocimiento y la Tecnología, 2015 A multi-modal search space can be defined as having multiple attraction basins – each basin has a single local optimum which is reached from all points in that basin when greedy local search is used.
Stephen Chen +3 more
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Precritical State Transition Dynamics in the Attractor Landscape of a Molecular Interaction Network Underlying Colorectal Tumorigenesis. [PDF]
PLoS ONE, 2015 From the perspective of systems science, tumorigenesis can be hypothesized as a critical transition (an abrupt shift from one state to another) between proliferative and apoptotic attractors on the state space of a molecular interaction network, for ...
Hyunho Chu, Daewon Lee, Kwang-Hyun Cho
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BASINS OF ATTRACTION FOR CASCADING MAPS [PDF]
International Journal of Bifurcation and Chaos, 2004 We study a finite uni-directional array of "cascading" or "threshold coupled" chaotic maps. We describe some of the attractors for such systems and prove general results about their basins of attraction. In particular, we show that the basins of attraction have infinitely many path components.
Boczko, Erik, Young, Todd
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Basin of Attraction Analysis of New Memristor-Based Fractional-Order Chaotic System
Complexity, 2021 Memristor is the fourth basic electronic element discovered in addition to resistor, capacitor, and inductor. It is a nonlinear gadget with memory features which can be used for realizing chaotic, memory, neural network, and other similar circuits and ...
Long Ding, Li Cui, Fei Yu, Jie Jin
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A Novel Chaos-Based Cryptography Algorithm and Its Performance Analysis
Mathematics, 2022 Data security represents an essential task in the present day, in which chaotic models have an excellent role in designing modern cryptosystems. Here, a novel oscillator with chaotic dynamics is presented and its dynamical properties are investigated ...
Ahmed A. Abd El-Latif +4 more
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BMC Bioinformatics, 2019 Background The ab initio approaches to protein structure prediction usually employ the Monte Carlo technique to search the structural conformation that has the lowest energy.
Chao Wang +6 more
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Riddled Basins of Attraction in Systems Exhibiting Extreme Events [PDF]
, 2017 Using a system of two FitzHugh-Nagumo units, we demonstrate the occurrence of riddled basins of attraction in delay-coupled systems as the coupling between the units is increased.
Feudel, Ulrike, Saha, Arindam
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