Identification of the Gray–Scott Model via Deterministic Learning

2021 ◽  
Vol 31 (04) ◽  
pp. 2150051
Author(s):  
Xunde Dong ◽  
Cong Wang
Keyword(s):  
Numerical Experiments ◽  
Interpolation Method ◽  
Reaction Diffusion ◽  
Spatiotemporal Chaos ◽  
Deterministic Learning ◽  
Novel Method ◽  
Global Identification ◽  
The Finite Difference Method ◽  
Two Phases ◽  
Identification Phase

Gray–Scott model is one of the most well-known reaction–diffusion models which has a wealth of spatiotemporal chaos behavior. It is commonly used to study spatiotemporal chaos. In the paper, a novel method is proposed for the identification of the Gray–Scott model via deterministic learning and interpolation. The method mainly consists of two phases: the local identification phase and the global identification phase. Local identification is achieved using the finite difference method and deterministic learning. Based on the local identification results, the interpolation method is employed to obtain global identification. Numerical experiments show the feasibility and effectiveness of the proposed method.

Spiral Tip Recognition via Deterministic Learning

2020 ◽  
Vol 30 (06) ◽  
pp. 2050093
Author(s):  
Chen Song ◽  
Xunde Dong ◽  
Cong Wang
Keyword(s):  
Numerical Simulations ◽  
Spiral Wave ◽  
Training Set ◽  
Deterministic Learning ◽  
Recognition Phase ◽  
Two Phases ◽  
Identification Phase

The spiral tip is vital to the understanding of the spiral wave behaviors. Most studies of spiral tip dynamics focused on the prevention, control, and elimination of spiral wave, while few studies focused on the recognition of spiral wave. In real systems with the spiral wave, the recognition of the spiral wave should be before control or elimination. In the paper, we study the recognition of the spiral tip via deterministic learning. It mainly consists of two phases: the identification phase and the recognition phase. In the identification phase, the dynamics of spiral tips of the training set is accurately identified by using deterministic learning. In the recognition phase, a set of errors is obtained for a test spiral tip by employing an estimator model. Finally, the recognition of test spiral tip is achieved according to the smallest error principle. Numerical simulations based on the spiral tip generated by the Barkley model are performed to demonstrate the effectiveness and feasibility of the proposed method.

Karhunen-Loève local characterization of spatiotemporal chaos in a reaction-diffusion system

2000 ◽  
Vol 61 (2) ◽  
pp. 1382-1385 ◽  
Author(s):  
Matthias Meixner ◽  
Scott M. Zoldi ◽  
Sumit Bose ◽  
Eckehard Schöll
Keyword(s):  
Reaction Diffusion ◽  
Spatiotemporal Chaos ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Local Characterization

scholarly journals A Novel Method to Determine the Local Stability of the n-Species Lotka-Volterra System with Multiple Delays

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Xiao-Ping Chen ◽  
Hao Liu
Keyword(s):  
Asymptotic Stability ◽  
Local Stability ◽  
Integral Method ◽  
Numerical Experiments ◽  
Positive Equilibrium ◽  
Multiple Delays ◽  
Volterra System ◽  
Local Asymptotic Stability ◽  
Discrete Delays ◽  
Novel Method

The n-species Lotka-Volterra system with discrete delays is considered. The local asymptotic stability of positive equilibrium is investigated based on a contour integral method. The main purpose of this paper is to propose a new and general algorithm to study the local asymptotic stability of the positive equilibrium for then-dimensional Lotka-Volterra system. Some numerical experiments are carried out to show the effectiveness of the proposed method.

scholarly journals Spatiotemporal chaos and quasipatterns in coupled reaction–diffusion systems

2020 ◽  
Vol 409 ◽  
pp. 132475 ◽  
Author(s):  
Jennifer K. Castelino ◽  
Daniel J. Ratliff ◽  
Alastair M. Rucklidge ◽  
Priya Subramanian ◽  
Chad M. Topaz
Keyword(s):  
Reaction Diffusion ◽  
Spatiotemporal Chaos ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Coupled Reaction

COEXISTENCE OF LOW- AND HIGH-DIMENSIONAL SPATIOTEMPORAL CHAOS IN A CHAIN OF DISSIPATIVELY COUPLED CHUA’S CIRCUITS

1994 ◽  
Vol 04 (03) ◽  
pp. 639-674 ◽  
Author(s):  
A.L. ZHELEZNYAK ◽  
L.O. CHUA
Keyword(s):  
Phase Space ◽  
Initial Conditions ◽  
Coupling Parameter ◽  
Reaction Diffusion ◽  
Cellular Neural Network ◽  
Spatiotemporal Chaos ◽  
Matrix Phase ◽  
High Dimensional ◽  
The Matrix ◽  
A Chain

Spatiotemporal dynamics of a one-dimensional cellular neural network (CNN) made of Chua’s circuits which mimics a reaction-diffusion medium is considered. An approach is presented to analyse the properties of this reaction-diffusion CNN through the characteristics of the attractors of an associated infinite-dimensional dynamical system with a matrix phase space. Using this approach, the spatiotemporal correlation dimension of the CNN’s spatiotemporal patterns is computed over various ranges of the diffusion coupling parameter, length of the chain, and initial conditions. It is shown that in a finite-dimensional projection of the matrix phase space of the CNN, both low- and high-dimensional attractors corresponding to different initial conditions coexist.

Application of the ICRP Database for Calculation of the Dose Coefficient for Aerosol Having Multimodal Particle Size Distribution

2020 ◽  
Vol 65 (1) ◽  
pp. 59-64
Author(s):  
A. Sukhoruchkin
Keyword(s):  
Particle Size ◽  
Aerosol Particle ◽  
Numerical Experiments ◽  
Interpolation Method ◽  
Linear Interpolation ◽  
Cumulative Distribution ◽  
Radioactive Aerosol ◽  
Dose Coefficient ◽  
True Value ◽  
Aerosol Particle Size

Purpose: Development of a method for calculating radioactive aerosol dose coefficient when the aerosol particle size measurements resulted in a multimodal radionuclide activity distribution by particle diameters. Material and methods: The physical prerequisite for the proposed method is that the multimodal distribution may be caused by the presence of several sources of aerosols with different particle sizes. In the ICRP database to each value of the aerosol dose coefficient there corresponds one of ten functions of log-normal (unimodal) distribution with specified parameters. In the developed method the result of the aerosol particle size measurement is approximated by the sum of said standard functions with weight factors of each of the functions defined such that the best least squares approximation is obtained. Then the dose coefficient of the aerosol under study is calculated based on the dose value additivity property, i.e. each weight factor is multiplied by a respective value of the dose coefficient from the ICRP database, and the obtained products are added up. Results: There was carried out a series of numerical experiments, in each of which “experimental” points were simply plotted on a graph of a certain cumulative distribution function. Coordinates of the points are used as input for the programme implementing the developed algorithm. The calculated dose coefficient value is compared with the true value and/or the value obtained with the linear interpolation method using the AMAD. Conclusion: Physical prerequisites and results of numerical experiments confirm the validity of the developed method.

Bifurcation Analysis and Spatiotemporal Patterns in a Diffusive Predator–Prey Model

2014 ◽  
Vol 24 (06) ◽  
pp. 1450081 ◽  
Author(s):  
Guangping Hu ◽  
Xiaoling Li ◽  
Shiping Lu ◽  
Yuepeng Wang
Keyword(s):  
Pattern Formation ◽  
Spiral Wave ◽  
Reaction Diffusion ◽  
Spatiotemporal Chaos ◽  
Diffusion System ◽  
Target Pattern ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
The Impact

In this paper, we consider a species predator–prey model given a reaction–diffusion system. It incorporates the Holling type II functional response and a quadratic intra-predator interaction term. We focus on the qualitative analysis, bifurcation mechanisms and pattern formation. We present the results of numerical experiments in two space dimensions and illustrate the impact of the diffusion on the Turing pattern formation. For this diffusion system, we also observe non-Turing structures such as spiral wave, target pattern and spatiotemporal chaos resulting from the time evolution of these structures.

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