Related papers: A Broad Dynamical Model for Pattern Formation by L…
The lac operon in Escherichia coli has been studied extensively and is one of the earliest gene systems found to undergo both positive and negative control. The lac operon is known to exhibit bistability, in the sense that the operon is…
We study the pattern dynamics in a reaction diffusion model of the activator--inhibitor type in the oscillatory regime. We consider finite systems with partially absorptive boundary conditions analizing examples in different geometries in…
A nonlinear time-delay model is proposed to describe the interaction dynamics between criminal and non-criminal populations, combining social influence mechanisms, saturation effects represented by a Holling type II functional response, and…
Notch signaling is a ubiquitous and versatile intercellular signaling system that drives collective behaviors and pattern formation in biological tissues. During embryonic development, Notch is involved in generation of collective…
Controlling laser-induced pattern formation remains a long-standing challenge. A key advance was recognising the pivotal role of intrinsic feedback mechanisms in self-organisation, which enabled self-similar patterns with long-range order…
Turing mechanisms can yield a large variety of patterns from noisy, homogenous initial conditions and have been proposed as patterning mechanism for many developmental processes. However, the molecular components that give rise to Turing…
The polarisation of cells and tissues is fundamental for tissue morphogenesis during biological development and regeneration. A deeper understanding of biological polarity pattern formation can be gained from the consideration of pattern…
Many complex mechatronic systems consist of multiple interconnected dynamical subsystems, which are designed, developed, analyzed, and manufactured by multiple independent teams. To support such a design approach, a modular model framework…
Oscillatory phase pattern formation and amplitude control for a linearized stochastic neuron field model was investigated by simulating coupled stochastic processes defined by stochastic differential equations. It was found, for several…
Cell motility in dense cell collectives is pivotal in various diseases like cancer metastasis and asthma. A central aspect in these phenomena is the heterogeneity in cell motility, but identifying the motility of individual cells is…
Mutualistic interactions are vital constituents of ecological and socio-economic systems. Empirical studies have found that the patterns of reciprocal relations among the participants often shows the salient features of being simultaneously…
Shapes of biological membranes are dynamically regulated in living cells. Although membrane shape deformation by proteins at thermal equilibrium has been extensively studied, nonequilibrium dynamics have been much less explored. Recently,…
Recent experiments have exploited elastic instabilities in membranes to create complex patterns. However, the rational design of such structures poses many challenges, as they are products of nonlinear elastic behavior. We pose a simple…
Recent experimental and theoretical studies suggest that crystallization and glass-like solidification are useful analogies for understanding cell ordering in confluent biological tissues. It remains unexplored how cellular ordering…
The Delta-Notch system plays a vital role in a number of areas in biology and typically forms a salt and pepper pattern in which cells strongly expressing Delta and cells strongly expressing Notch are alternately aligned via lateral…
A certain degree of inhibition is a common trait of dynamical networks in nature, ranging from neuronal and biochemical networks, to social and technological networks. We study here the role of inhibition in a representative dynamical…
Despite simplicity, the synchronous cellular automaton [D.A. Young, Math. Biosci. 72, 51 (1984)] enables reconstructing basic features of patterns of skin. Our extended model allows studying the formatting of patterns and their temporal…
Multicellular tissues are the building blocks of many biological systems and organs. These tissues are not static, but dynamically change over time. Even if the overall structure remains the same there is a turnover of cells within the…
When a nematic liquid crystal is confined in a porous medium with strong anchoring conditions, topological defects, called disclinations, are stably formed with numerous possible configurations. Since the energy barriers between them are…
Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…