21 papers · ranked by Valyu relevance
Yuzuru Kato, Hiroya Nakao
Turing instability is a fundamental mechanism of nonequilibrium self-organization. However, despite the universality of its essential mechanism, Turing instability has thus far been investigated mostly in classical systems. In this study, we show that Turing instability can occur in a quantum dissipative system and…
Timotéo Carletti, Riccardo Muolo
We hereby develop the theory of Turing instability for reaction-diffusion systems defined on complex networks assuming finite propagation. Extending to networked systems the framework introduced by Cattaneo in the 40's, we remove the unphysical assumption of infinite propagation velocity holding for reaction-diffusion…
Robert Jencks
Turing Instability Authors: ['Robert Jencks'] - Characterization of Turing instability in a ring-based ODE model for zebrafish. - Quantitative analysis for 4 main parameters, including any finite number of cells, N. - Stability curves for large N differ substantially from previous PDE model. - Critical melanophore…
Vit Piskovsky
In this paper, I prove necessary and sufficient conditions for the existence of Turing instabilities in a general system with three interacting species. Turing instabilities describe situations when a stable steady state of a reaction system (ordinary differential equation) becomes an unstable homogeneous steady state…
Hazlam S. Ahmad Shaberi, Aibek Kappassov, Antonio Matas-Gil, Robert G. Endres
'Robert G. Endres'] Many cellular patterns exhibit a reaction-diffusion component, suggesting that Turing instability may contribute to pattern formation. However, biological gene-regulatory pathways are more complex than simple Turing activator-inhibitor models and generally do not require fine-tuning of parameters as…
Carsten Conradi, Maya Mincheva, Hannes Uecker
We study the onset of spatial instabilities in reaction networks where the spatially homogeneous system admits a steady state parameterization. We formulate a sufficient condition -- based on the signs of the constant and leading coefficients of the characteristic polynomial of the linearized Jacobian scaled by the…
Damian G. Kelty‐Stephen, Madhur Mangalam
Turing inspired a computer metaphor of the mind and brain that has been handy and has spawned decades of empirical investigation, but he did much more and offered behavioral and cognitive sciences another metaphor—that of the cascade. The time has come to confront Turing's cascading instability, which suggests a…
H. O. Fatoyinbo, R. G. Brown, D. J. W. Simpson, B. van Brunt
Spatiotemporal patterns are common in biological systems. For electrically coupled cells, previous studies of pattern formation have mainly used applied current as the primary bifurcation parameter. The purpose of this paper is to show that applied current is not needed to generate spatiotemporal patterns for smooth…
Nirmali Das, István Balázs, Bornali Das, Gergely Röst
This study investigates how the interaction between gene expression time delay and domain size governs spatio-temporal pattern formation in a reaction-diffusion system. To investigate these phenomena, we utilize a modified version of the Schnakenberg model called the LI (ligand internalisation) model. In a…
Marie Dorchain, S. Nirmala Jenifer, Timotéo Carletti
We are surrounded by spatio-temporal patterns resulting from the interaction of the numerous basic units constituting natural or human-made systems. In presence of diffusive-like coupling, Turing theory has been largely applied to explain the formation of such self-organized motifs both on continuous domains or…
Yuzuru Kato, Hiroya Nakao
Turing instability is a fundamental mechanism of nonequilibrium self-organization. However, despite the universality of its essential mechanism, Turing instability has thus far been investigated mostly in classical systems. In this study, we show that Turing instability can occur in a quantum dissipative system and…
Hazlam S. Ahmad Shaberi, Aibek Kappassov, Antonio Matas-Gil, Robert G. Endres
Many cellular patterns exhibit a reaction-diffusion component, suggesting that Turing instability may contribute to pattern formation. However, biological gene-regulatory pathways are more complex than simple Turing activator-inhibitor models and generally do not require fine-tuning of parameters as dictated by the…
Priya Chakraborty, Subrata Dey, Ranu Kundu, Malay Banerjee + 1 more
Exploring the emergence of spatio-temporal patterns due to nonlinearities in gene expression is a relatively new development. In this work, we explore the effect of resource constraint on gene regulatory motif from both equilibrium and spatio-temporal standpoint, taking into consideration the degradation class of…
Jurgen Riedel, Chris P. Barnes
In this study we examine the emergence of complex biological patterns through the lens of reaction-diffusion systems. We introduce two novel complexity metrics, Diversity of Number of States (DNOS) and Diversity of Pattern Complexity (DPC), which aim to quantify structural intricacies in pattern formation, enhancing…
Yanhua Zhu, Xiangyi Ma, Jinliang Wang, Federico Frascoli + 1 more
The mussel-algae (M-A) system plays a crucial role in maintaining the balance of marine aquaculture ecosystems. Mussels filter algae from the water as a food source, while algae produce oxygen through photosynthesis and contribute to nutrient cycling. Fluctuations in the density and spatial distribution of algae…
Edgardo Villar-Sepúlveda, Alan R. Champneys
Necessary and sufficient conditions are provided for a diffusion-driven instability of a stable equilibrium of a reaction-diffusion system with n components and diagonal diffusion matrix. These can be either Turing or wave instabilities. Known necessary and sufficient conditions are reproduced for there to exist…
Marie Dorchain, Riccardo Muolo, Timotéo Carletti
Self-organization in natural and engineered systems causes the emergence of ordered spatiotemporal motifs. In presence of diffusive species, Turing theory has been widely used to understand the formation of such patterns on continuous domains obtained from a diffusion-driven instability mechanism. The theory was later…
Jurgen Riedel, Chris P. Barnes
In this study we examine the emergence of complex biological patterns through the lens of reaction-diffusion systems. We introduce two novel complexity metrics — Diversity of Number of States (DNOS) and Diversity of Pattern Complexity (DPC)— which aim to quantify structural intricacies in pattern formation, enhancing…
Laura Regueira López de Garayo, Luciano Marcon
Understanding how genetic networks can drive different self-organizing spatial behaviors remains a significant challenge. Here, we use an automated algebraic method to systematically screen for Turing networks capable of generating diverse spatial patterns from noise, including periodic static waves, traveling waves…
Neetu ., Aman Saini, Rishi Ram Mahato, Priyanka . + 1 more
The theory behind origin of life to Darwinian evolution considers emergence of dissipative structures driven by the flow of energy across all length scales. To this end, developing and deeper understanding of non-equilibrium self-assembly processes under continuous supply of energy is a demanding matter, both in…
Khulood Al-sakkaf, Monicka Kullappan, Manoj Chaudhury
Recent studies demonstrated that an elastomer containing hygroscopic inclusions absorbs moisture and swell. Here we show that a thin film of such an elastomer bonded to a rigid substrate undergoes morphological instability upon absorption of water, the wavelength of which increases linearly with its thickness. As the…