New way for cell differentiation: Reaction, diffusion and chaotic waves

Robust morphogenesis by chaotic dynamics

“…In the section on the methods, we show (following the study 13 ) how chaotic attractors can serve as cellular developmental programs (CDPs) and create complicated spatiotemporal cell patterns. Therefore, it is shown that dynamical systems are given by Eq.…”

“…We use the results of the work 11 – 13 and it can be described as follows. The idea can be illustrated by Fig.…”

“…The conditions can be satisfied if the time evolution of the amplitudes corresponding to segments located at the j -th cell is governed by chaotic (or stochastic) dynamics. Note that the precise choice of this dynamics plays no role, but the corresponding attractor should be ergodic and mixing 13 .…”

Meeting of Chemical Wave Fronts Creates Chaos

“…Note that numerical simulations show that chaotic waves exist for realistic models of population dynamics; see [14]. They extend our possibilities in pattern formation and can be applied for pattern coding and morphogenesis problems; see [20,21]. A key difference between chaotic waves and usual travelling fronts can be understood if we consider the somitogenesis problem [22][23][24].…”

“…However, such a model permits us to explain only how periodical gene expression oscillations encode periodical layers. To encode arbitrary patterns we need waves with chaotic dynamics [21]. Chaotic waves also help in practical problems of pattern coding [20].…”