Nonlinear dynamics of full-range CNNs with time-varying delays and variable coefficients

In the article, the dynamical behaviours of the full-range cellular neural networks (FRCNNs) with variable coefficients and time-varying delays are considered. Firstly, the improved model of the FRCNNs is proposed, and the existence and uniqueness of the solution are studied by means of differential inclusions and set-valued analysis. Secondly, by using the Hardy inequality, the matrix analysis, and the Lyapunov functional method, we get some criteria for achieving the globally exponential stability (GES). Finally, some examples are provided to verify the correctness of the theoretical results

A study on semiflows generated by cooperative full-range CNNs

The paper considers the full-range (FR) model of cellular neural networks (CNNs) characterized by ideal hard-limiter nonlinearities with two vertical segments in the current–voltage characteristic. It is shown that when the FRCNNs are cooperative, i.e., there are excitatory interconnections between distinct neurons, the generated solution semiflow is monotone and that monotonicity implies some fundamental restrictions on the geometry of omega-limit sets. The result on monotonicity is a generalization to the class of differential inclusions describing the dynamics of FRCNNs of a classic result due to Kamke for cooperative ordinary differential equations. The paper also points out difficulties to use the standard theory of eventually strongly monotone (ESM) semiflows for addressing convergence of FRCNNs. By means of counterexamples, it is shown that, even assuming the irreducibility of the interconnections, the semiflow generated by a cooperative FRCNN is not ESM; furthermore, also the limit set dichotomy can be violated

Modelling the role of polarity and geometry in cell-fate dynamics of mammary organoids

Mammary organoids are three-dimensional structures that are derived from mammary gland cells and can recapitulate the complex architecture and functionality of the mammary gland in vitro. Mammary organoids hold great promise for advancing our understanding of mammary gland biology, breast cancer, and precision medicine. However, phenotypic and genetic instabilities observed in long-term expansion limit their applications to prolonged experiments and large-scale production. A proposed factor driving this organoid-wise heterogeneity is plasticity within mammary epithelial cells, the phenotypic switching of cells. Therefore, we examine the dynamics of key intracellular pathways that govern cell-fate commitment in mammary organoids. Specifically, we explore the influence of local tissue geometry and polarity in cell-cell signalling in stabilising cell-fate determinants using a combination of analytic and numerical multiscale modelling approaches. We introduce interconnected dynamical systems, graph-coupled dynamical systems with input-output representations to describe intercellular signal flow between cells. Exploiting structural properties of the bilayer graphs describing mammary tissue architecture, we derive low-dimensional forms of these models enabling the analytic examination of the interplay of structure and polarity on cell-fate patterning, extending existing methods to include pathway crosstalk and providing rigorous links between low-dimensional and their associated large-scale representations. Supporting the analytic investigations of static spatial domains with cellbased modelling, we provide evidence that sufficiently strong cell-cell signal polarity has the capacity to generate and sustain bilayer laminar patterns of Notch1, a critical cell-fate determinant and inducer of plasticity in mammary epithelial cells. Furthermore, we demonstrate how local tissue curvature can relax the constraints of polarity supporting healthy tissue growth and supporting branching morphologies. Fundamentally, this study highlights the significance of cell signalling polarity as a control mechanism of cell-fate commitment. Thus, the establishment and maintenance of epithelial polarity should be considered in long-term mammary organoid expansion protocol development