Related papers: Classification of instabilities for the nonideal B…
We carry out a comprehensive linear stability analysis of active Brownian particle systems around a constant homogeneous state. These scalar models, being important prototypes for the continuous description of active matter, are…
This paper investigates the conditions for the stability and emergence of patterns in a new three-component reaction-diffusion system. The system describes the coexistence and interaction of water reservoirs, vegetation, and bushfire…
A class of hyperbolic reaction--diffusion models with cross-diffusion is derived within the context of Extended Thermodynamics. Linear stability analysis is performed to study the nature of the equilibrium states against uniform and…
Differential diffusion is a source of instability in population dynamics systems when species diffuse with different rates. Predator-prey systems show this instability only under certain specific conditions, usually requiring Holling-type…
We develop a theory for thermodynamic instabilities of complex fluids composed of many interacting chemical species organised in families. This model includes partially structured and partially random interactions and can be solved exactly…
Reaction diffusion systems are often used to study pattern formation in biological systems. However, most methods for understanding their behavior are challenging and can rarely be applied to complex systems common in biological…
Turing instabilities of reaction-diffusion systems can only arise if the diffusivities of the chemical species are sufficiently different. This threshold is unphysical in most systems with $N=2$ diffusing species, forcing experimental…
Biomolecular processes are typically modeled using chemical reaction networks coupled to infinitely large chemical reservoirs. A difference in chemical potential between these reservoirs can drive the system into a non-equilibrium steady…
Applying the Lyapunov-Schmidt reduction approach introduced by Mielke and Schneider in their analysis of the fourth-order scalar Swift-Hohenberg equation, we carry out a rigorous small-amplitude stability analysis of Turing patterns for the…
We establish the connection between thermodynamic and dynamical instabilities in relativistic hydrodynamics with multiple flavours of conserved U(1) charges. In theories with positive hydrodynamic entropy production, where the underlying…
For an activator-inhibitor reaction-diffusion system in a bounded three-dimensional domain $\Omega$ of $O(1)$ volume and small activator diffusivity of $O(\varepsilon^2)$, we employ a hybrid asymptotic-numerical method to investigate two…
Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the…
Chemical reaction networks can undergo nonequilibrium phase transitions upon variation of external control parameters like the chemical potential of a species. We investigate the flux in the associated chemostats that is proportional to the…
In a system of non-linear chemical reactions called the Brusselator, we show that {\it intrinsic noise} can be regulated to drive it to exhibit resonance in the presence of a sub-threshold signal. The phenomena of periodic stochastic…
Patterns in reaction-diffusion systems near primary bifurcations can be studied locally and classified by means of amplitude equations. This is not possible for excitable reaction-diffusion systems. In this Letter we propose a global…
This paper investigates pattern formation in reaction--diffusion systems with both diffusive and nondiffusive components, providing necessary and sufficient conditions for diffusion-driven instability (DDI) and establishing the existence of…
The concept of cross diffusion is applied to some biological systems. The conditions for persistence and Turing instability in the presence of cross diffusion are derived. Many examples including: predator-prey, epidemics (with and without…
The dynamics of randomly crosslinked liquids is addressed via a Rouse- and a Zimm-type model with crosslink statistics taken either from bond percolation or Erdoes-Renyi random graphs. While the Rouse-type model isolates the effects of the…
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…
An effective Hartree-Fock-Bogoliubov-type interaction is calculated for the Hubbard-model in second order in the coupling by means of flow-equations. A stability analysis is performed in order to obtain the transition into various possible…