Study on the Compatibility of Multi-Bifurcations by Simulations of Pattern Formation
IEEE Access, 2019 Bifurcation is considered the main mathematical mechanism for the formation of spatial self-organizing patterns in many studies. When bifurcation was initially defined, only the transition of the system from stable state to unstable state or from uniform
Feifan Zhang +4 more
doaj +1 more source
Steady-state bifurcation of FHN-type oscillator on a square domain
Nonlinear Analysis, 2023 The Turing patterns of reaction-diffusion equations defined over a square region are more complex because of the D4-symmetry of the spatial region. This leads to the occurrence of multiple equivariant Turing bifurcations.
Chunrui Zhang +2 more
doaj +1 more source
Pattern formation driven by cross--diffusion in a 2D domain
, 2012 In this work we investigate the process of pattern formation in a two dimensional domain for a reaction-diffusion system with nonlinear diffusion terms and the competitive Lotka-Volterra kinetics. The linear stability analysis shows that cross-diffusion,
Gambino, G. +2 more
core +1 more source
Two-dimensional localized structures in harmonically forced oscillatory systems [PDF]
, 2016 Two-dimensional spatially localized structures in the complex Ginzburg–Landau equation with 1:1 resonance are studied near the simultaneous presence of a steady front between two spatially homogeneous equilibria and a supercritical Turing bifurcation on ...
Knobloch, Edgar, Ma, Yi-Ping
core +1 more source
Size‐Modulated Mesoderm‐Endoderm Divergence and Myocardial Cavitation in Micropatterned Cardioids
Advanced Science, EarlyView.Micropatterned cardioids, CRISPR‐engineered reporter hiPSCs, deep‐tissue imaging, and single‐cell RNA sequencing are integrated to model mesoderm‐endoderm co‐development. Heart‐foregut crosstalk promotes single large cavitation inside cardioids, resembling early heart chamber formation. ABSTRACT The human heart, originating from the splanchnic mesoderm,
Plansky Hoang +12 more
wiley +1 more source
Turing Instability and Pattern Formation in an Activator-Inhibitor System with Nonlinear Diffusion
, 2014 In this work we study the effect of density dependent nonlinear diffusion on pattern formation in the Lengyel--Epstein system. Via the linear stability analysis we determine both the Turing and the Hopf instability boundaries and we show how nonlinear ...
Gambino, G. +2 more
core +1 more source
Spatio-temporal dynamics induced by competing instabilities in two asymmetrically coupled nonlinear evolution equations [PDF]
, 2014 Pattern formation often occurs in spatially extended physical, biological and chemical systems due to an instability of the homogeneous steady state.
A. Torcini +5 more
core +3 more sources
Material‐Based Intelligence: Autonomous Adaptation and Embodied Computation in Physical Substrates
Advanced Intelligent Systems, EarlyView.This perspective formulates a unifying framework for Material‐Based Intelligence (MBI), defining the physical requirements for materials to achieve embodied action, active memory and embodied information processing through intrinsic nonequilibrium dynamics. The design of intelligent materials often draws parallels with the complex adaptive behaviors of
Vladimir A. Baulin +4 more
wiley +1 more source
, 2011 Competition of spatial and temporal instabilities under time delay near the codimension-two Turing-Hopf bifurcations is studied in a reaction-diffusion equation.
Hui-Juan Wang +4 more
core +1 more source
Turing Bifurcation and Pattern Formation of Stochastic Reaction-Diffusion System [PDF]
Advances in Mathematical Physics, 2017 Noise is ubiquitous in a system and can induce some spontaneous pattern formations on a spatially homogeneous domain. In comparison to the Reaction-Diffusion System (RDS), Stochastic Reaction-Diffusion System (SRDS) is more complex and it is very difficult to deal with the noise function.
Qianiqian Zheng +3 more
openaire +3 more sources