Related papers: Diversity, Stability, Recursivity, and Rule Genera…

We investigate the oscillatory dynamics and bifurcation structure of a reaction-diffusion system with bistable nonlinearity and mass conservation, which was proposed by [Otsuji et al, PLoS Comp. Biol. 3 (2007), e108]. The system is a useful…

Understanding the rules underlying organismal development is a major unsolved problem in biology. Each cell in a developing organism responds to signals in its local environment by dividing, excreting, consuming, or reorganizing, yet how…

Mathematical models of stem cell differentiation are commonly based upon the concept of subsequent cell fate decisions, each controlled by a gene regulatory network. These networks exhibit a multistable behavior and cause the system to…

Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…

We disclose the generality of the intrinsic mechanisms underlying multistability in reciprocally inhibitory 3-cell circuits composed of simplified, low-dimensional models of oscillatory neurons, as opposed to those of a detailed Hodgkin-…

Stochastic dynamics govern many important processes in cellular biology, and an underlying theoretical approach describing these dynamics is desirable to address a wealth of questions in biology and medicine. Mathematical tools exist for…

We consider a model system of persistent random walkers that can jam, pass through each other or jump apart (recoil) on contact. In a continuum limit, where particle motion between stochastic changes in direction becomes deterministic, we…

In many adult tissues, stem cells and differentiated cells are not homogeneously distributed : stem cells are arranged in periodic "niches", and differentiated cells are constantly produced and migrate out of these niches. In this article,…

A first-principles theory is developed for the general evolution of a key structural characteristic of planar granular systems - the cell order distribution. The dynamic equations are constructed and solved in closed form for a number of…

In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…

Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…

There are many natural, physical, and biological systems that exhibit multiple time scales. For example, the dynamics of a population of ticks can be described in continuous time during their individual life cycle yet discrete time is used…

The dynamic instability of the living systems and the "superposition" of different forms of randomness are viewed as a component of the contingently increasing organization of life along evolution. We briefly survey how classical and…

Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing's reaction--diffusion theory, which connects cellular signalling and transport…

We study molecular dynamics within populations of diffusively coupled cells under the assumption of fast diffusive exchange. As a technical tool, we propose conditions on boundedness and ultimate boundedness for systems with a singular…

We consider a specific dynamical system of groups formation. It is based simultaneously on a gradient competition between groups and a strong accumulation inside groups. Such a dynamical system demonstrates interesting behavior of densities…

A fundamental issue discussed in evolutionary biology is the transition from unicellular to multicellular organisms. Here we develop non-robust models provided in [1] and attempt to get robust models investigated how differentiation of…

Cells are able to generate phenotypic diversity both during development and in response to stressful and changing environments, aiding survival. The biologically and medically vital process of a cell assuming a functionally important fate…

We propose a principle of consistency between different hierarchical levels of biological systems. Given a consistency between molecule replication and cell reproduction, universal statistical laws on cellular chemical abundances are…

Complex evolving systems such as the biosphere, ecosystems and societies exhibit sudden collapses, for reasons that are only partially understood. Here we study this phenomenon using a mathematical model of a system that evolves under…