Toward an interpretation of dynamic neural activity in terms of chaotic dynamical systems
I Tsuda - Behavioral and Brain Sciences, 2001 - cambridge.org
Using the concepts of chaotic dynamical systems, we present an interpretation of dynamic
neural activity found in cortical and subcortical areas. The discovery of chaotic itinerancy in …
neural activity found in cortical and subcortical areas. The discovery of chaotic itinerancy in …
Mechanism of branching morphogenesis inspired by diatom silica formation
The silica-based cell walls of diatoms are prime examples of genetically controlled, species-
specific mineral architectures. The physical principles underlying morphogenesis of their …
specific mineral architectures. The physical principles underlying morphogenesis of their …
Rise and fall of periodic patterns for a generalized Klausmeier–Gray–Scott model
In this paper we introduce a conceptual model for vegetation patterns that generalizes the
Klausmeier model for semi-arid ecosystems on a sloped terrain (Klausmeier in Science 284 …
Klausmeier model for semi-arid ecosystems on a sloped terrain (Klausmeier in Science 284 …
Physics-informed neural networks approach for 1D and 2D Gray-Scott systems
Abstract Nowadays, in the Scientific Machine Learning (SML) research field, the traditional
machine learning (ML) tools and scientific computing approaches are fruitfully intersected for …
machine learning (ML) tools and scientific computing approaches are fruitfully intersected for …
Unified framework for localized patterns in reaction–diffusion systems; the Gray–Scott and Gierer–Meinhardt cases
F Al Saadi, A Champneys - Philosophical Transactions of …, 2021 - royalsocietypublishing.org
A recent study of canonical activator-inhibitor Schnakenberg-like models posed on an
infinite line is extended to include models, such as Gray–Scott, with bistability of …
infinite line is extended to include models, such as Gray–Scott, with bistability of …
Hopf bifurcations and oscillatory instabilities of spike solutions for the one-dimensional Gierer-Meinhardt model
In the limit of small activator diffusivity ɛ, the stability of symmetric k-spike equilibrium
solutions to the Gierer-Meinhardt reaction-diffusion system in a one-dimensional spatial …
solutions to the Gierer-Meinhardt reaction-diffusion system in a one-dimensional spatial …
The stability and dynamics of localized spot patterns in the two-dimensional Gray–Scott model
W Chen, MJ Ward - SIAM Journal on Applied Dynamical Systems, 2011 - SIAM
The dynamics and stability of multispot patterns to the Gray–Scott (GS) reaction-diffusion
model in a two-dimensional domain is studied in the singularly perturbed limit of small …
model in a two-dimensional domain is studied in the singularly perturbed limit of small …
Provenance of life: Chemical autonomous agents surviving through associative learning
S Bartlett, D Louapre - Physical Review E, 2022 - APS
We present a benchmark study of autonomous, chemical agents exhibiting associative
learning of an environmental feature. Associative learning systems have been widely …
learning of an environmental feature. Associative learning systems have been widely …
A new class of stopping self-sustained waves: a factor determining the spatial dynamics of blood coagulation
FI Ataullakhanov, VI Zarnitsyna… - Physics …, 2002 - iopscience.iop.org
Two self-sustained wave regimes newly found in blood coagulation models are
discussed:(1) oscillating-amplitude self-sustained waves, and (2) waves initially propagating …
discussed:(1) oscillating-amplitude self-sustained waves, and (2) waves initially propagating …
High-fidelity simulations for Turing pattern formation in multi-dimensional Gray–Scott reaction-diffusion system
In this study, the authors present high-fidelity numerical simulations for capturing the Turing
pattern in a multi-dimensional Gray–Scott reaction-diffusion system. For this purpose, an …
pattern in a multi-dimensional Gray–Scott reaction-diffusion system. For this purpose, an …