Related papers: A Cayley Tree Immune Network Model with Antibody D…
The uncertainty of multidimensional shift spaces draws attracted attention of researchers. For example, the emptiness problem is undecidable; there exist aperiodic shifts of finite type; there is a nonempty shift of finite type exhibiting…
Many pathogens spread primarily via direct contact between infected and susceptible hosts. Thus, the patterns of contacts or contact network of a population fundamentally shapes the course of epidemics. While there is a robust and growing…
Data of physical contacts and face-to-face communications suggest temporally varying networks as the media on which infections take place among humans and animals. Epidemic processes on temporal networks are complicated by complexity of…
The asymmetric Hopfield model is used to simulate signaling dynamics in gene/transcription factor networks. The model allows for a direct mapping of a gene expression pattern into attractor states. We analyze different control strategies…
We extensively explore networks of weakly unbalanced, leaky integrate-and-fire (LIF) neurons for different coupling strength, connectivity, and by varying the degree of refractoriness, as well as the delay in the spike transmission. We find…
An input-output model for networks with link uncertainty is developed. The main result presents a set of integral quadratic constraints (IQCs) that collectively imply robust stability of the uncertain network dynamics. The model dependency…
The dynamics of complex systems generally include high-dimensional, non-stationary and non-linear behavior, all of which pose fundamental challenges to quantitative understanding. To address these difficulties we detail a new approach based…
We introduce a growing network evolution model with nodal attributes. The model describes the interactions between potentially violent V and non-violent N agents who have different affinities in establishing connections within their own…
Despite significant progress on stability analysis of conventional multiagent networked systems with weakly coupled state-network dynamics, most of the existing results have shortcomings in addressing multiagent systems with highly coupled…
We address the role of community structure of an interaction network in ordering dynamics, as well as associated forms of metastability. We consider the voter and AB model dynamics in a network model which mimics social interactions. The AB…
We consider a model in which a collective state couples to a large number of background states. The background states can be chosen to have properties which are classically characterized as regular or chaotic. We found that the dynamical…
We consider a model of dynamics of the immune system. The model is based on three factors: occasional boosting and continuous waning of immunity and a general description of the period between subsequent boosting events. The antibody…
Mathematical modeling and analysis can provide insight on the dynamics of ecosystems which maintain biodiversity in the face of competitive and prey-predator interactions. Of primary interests are the underlying structure and features which…
Based on extensive study of a dynamical systems model of the development of a cell society, a novel theory for stem cell differentiation and its regulation is proposed as the ``chaos hypothesis''. Two fundamental features of stem cell…
Social movements, neurons in the brain or even industrial suppliers are best described by agents evolving on networks with basic interaction rules. In these real systems, the connectivity between agents corresponds to the a critical state…
The Kronig-Penney model is used to Study the effect of nonlinear interaction on the transmissive properties of both ordered and disordered chains. In the ordered case, the nonlinearity can either localize or delocalize the electronic states…
There is increasing interest in developing the theoretical foundations of networked control systems that illuminate how brain networks function so as to enable sensory perception, control of movement, memory and all the operations that are…
Structured populations are ubiquitous across the biological sciences. Mathematical models of these populations allow us to understand how individual physiological traits drive the overall dynamics in aggregate. For example, linear age- or…
Compartmental models have long served as important tools in mathematical epidemiology, with their usefulness highlighted by the recent COVID-19 pandemic. However, most of the classical models fail to account for certain features of this…
We study a simplified model of monoclonal antibodies confined in a patchy random porous medium. Antibodies are represented as Y-shaped particles composed of seven tangential hard spheres with attractive patches on the terminal beads, while…