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We consider a one-dimensional directional array of diffusively coupled oscillators. They are perturbed by the injection of a small additive noise, typically orders of magnitude smaller than the oscillation amplitude, and the system is…
The fundamental biological processes of development of tissues and organs in multicellular organisms is governed by various signaling molecules, which are called morphogens. It is known that spatial and temporal variations in concentration…
We study the Swift-Hohenberg equation - a paradigm model for pattern formation - with "large" spatially periodic coefficients and find a Turing bifurcation that generates patterns whose leading order form is a Bloch wave modulated by…
We propose a general theory for surface patterning in many different biological systems, including mite and insect cuticles, pollen grains, fungal spores, and insect eggs. The patterns of interest are often intricate and diverse, yet an…
Heteroclinic structures organize global features of dynamical systems. We analyze whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more…
Neurons process sensory stimuli efficiently, showing sparse yet highly variable ensemble spiking activity involving structured higher-order interactions. Notably, while neural populations are mostly silent, they occasionally exhibit highly…
We consider a heteroclinic network in the framework of winnerless competition of species. It consists of two levels of heteroclinic cycles. On the lower level, the heteroclinic cycle connects three saddles, each representing the survival of…
Linear response theory has found many applications in statistical physics. One of these is to compute minimal-work protocols that drive nonequilibrium systems between different thermodynamic states, which are useful for designing engineered…
Pattern forming systems allow for a wealth of states, where wavelengths and orientation of patterns varies and defects disrupt patches of monocrystalline regions. Growth of patterns has long been recognized as a strong selection mechanism.…
Many physical systems involve two types of orientational order, which are coupled together. For example, ferroelectric nematic liquid crystals have coupled polar and nematic order, and tilted hexatic phases have coupled polar and hexatic…
Neuronal systems need to process temporal signals. We here show how higher-order temporal (co-)fluctuations can be employed to represent and process information. Concretely, we demonstrate that a simple biologically inspired feedforward…
Modelling the dynamics of dense granular media is a long standing challenge and essential to many natural phenomena and technological applications. Here, we trace back puzzling experimental observation of detailed-balanced steady states to…
Turing theory of pattern formation is among the most popular theoretical means to account for the variety of spatio-temporal structures observed in Nature and, for this reason, finds applications in many different fields. While Turing…
Understanding cell fate selection remains a central challenge in developmental biology. We present a class of simple yet biologically-motivated mathematical models for cell differentiation that generically generate oscillations and hence…
It is well known that the classical energetically consistent micropolar model has limits in simulating the frequency band structure of packed granular materials (see Merkel et al., 2011). It is here shown that if a standard continualization…
Most recent advances in machine learning and analytics for process control pose the question of how to naturally integrate new data-driven methods with classical process models and control. We propose a process modeling framework enabling…
According to empirical observations, some pattern formation phenomena in driven many-particle systems are more pronounced in the presence of a certain noise level. We investigate this phenomenon of fluctuation-driven ordering with a…
The importance of higher-order relations is widely recognized in a large number of real-world systems. However, annotating them is a tedious and sometimes impossible task. Consequently, current approaches for data modelling either ignore…
We investigate the dynamics of cellular solidification patterns using three-dimensional phase-field simulations. The cells can organize into stable hexagonal patterns or exhibit unsteady evolutions. We identify the relevant secondary…
A novel mechanism for cell differentiation is proposed, based on the dynamic clustering in a globally coupled chaotic system. A simple model with metabolic reaction, active transport of chemicals from media, and cell division is found to…