Related papers: Turing patterns mediated by network topology in ho…
We numerically solve the active nematohydrodynamic equations of motion, coupled to a Turing reaction-diffusion model, to study the effect of active nematic flow on the stripe patterns resulting from a Turing instability. If the activity is…
A central issue in the study of large complex network systems, such as power grids, financial networks, and ecological systems, is to understand their response to dynamical perturbations. Recent studies recognize that many real networks…
Many existing studies on pattern formation in the reaction-diffusion systems rely on deterministic models. However, environmental noise is often a major factor which leads to significant changes in the spatiotemporal dynamics. In this…
In this paper, we investigate the emergence of a predator-prey system with Ivlev-type functional response and reaction-diffusion. We study how diffusion affects the stability of predator-prey coexistence equilibrium and derive the…
There is growing recognition that the network structures arising from interactions between different entities in physical, social and biological systems fundamentally alter the evolutionary outcomes. Previous paradigm exploring evolutionary…
Pattern formation and evolution in unsynchronizable complex networks are investigated. Due to the asymmetric topology, the synchronous patterns formed in complex networks are irregular and nonstationary. For coupling strength immediately…
The lack of large-scale, continuously evolving empirical data usually limits the study of networks to the analysis of snapshots in time. This approach has been used for verification of network evolution mechanisms, such as preferential…
In some systems, the behavior of the constituent units can create a `context' that modifies the direct interactions among them. This mechanism of indirect modification inspired us to develop a minimal model of context-dependent spreading.…
Functional networks provide a topological description of activity patterns in the brain, as they stem from the propagation of neural activity on the underlying anatomical or structural network of synaptic connections. This latter is well…
Dynamic networks are structured interconnections of dynamical systems (modules) driven by external excitation and disturbance signals. In order to identify their dynamical properties and/or their topology consistently from measured data, we…
Climate change is reshaping species interactions and movement across fragmented landscapes. Despite this, most mathematical models assume random diffusion, overlooking the influence of directed movement. Here, we develop a graph based…
This work examines the problem of topology inference over discrete-time nonlinear stochastic networked dynamical systems. The goal is to recover the underlying digraph linking the network agents, from observations of their state-evolution.…
Models of simple excitable dynamics on graphs are an efficient framework for studying the interplay between network topology and dynamics. This subject is a topic of practical relevance to diverse fields, ranging from neuroscience to…
Many social and biological systems are characterized by enduring hierarchies, including those organized around prestige in academia, dominance in animal groups, and desirability in online dating. Despite their ubiquity, the general…
Spatial pattern formation is a key feature of many natural systems in physics, chemistry and biology. The essential theoretical issue in understanding pattern formation is to explain how a spatially homogeneous initial state can undergo…
Network science can offer fundamental insights into the structural and functional properties of complex systems. For example, it is widely known that neuronal circuits tend to organize into basic functional topological modules, called…
We investigate global stability and dynamics of large ecological networks by classical methods of the dynamical system theory, including Hamiltonian methods, and averaging. Our analysis exploits the network topological structure, namely,…
Reaction-diffusion systems have been proposed as a model for pattern formation and morphogenesis. The Fickian diffusion typically employed in these constructions model the Brownian motion of particles. The biological and chemical elements…
The Turing mechanism describes the emergence of spatial patterns due to spontaneous symmetry breaking in reaction-diffusion processes and underlies many developmental processes. Identifying Turing mechanisms in biological systems defines a…
We estimate density of defects frozen into a biological Turing pattern which was turned on at a finite rate. A self-locking of gene expression in individual cells, which makes the Turing transition discontinuous, stabilizes the pattern…