Related papers: Delayed coupling theory of vertebrate segmentation
A stretched DNA molecule which is also under- or overwound, undergoes a buckling transition forming intertwined looped domains called plectonemes. Here we develop a simple theory that extends the two-phase model of stretched supercoiled…
Processing sequential inputs is a fundamental brain function, underlying tasks such as sensory perception, language, and motor control. A challenge in sequence processing is to represent not only the order of events, but also their precise…
The epigenetic pathway of a cell as it differentiates from a stem cell state to a mature lineage-committed one has been historically understood in terms of Waddington's landscape, consisting of hills and valleys. The smooth top and…
Many organisms possess both a cell cycle to control DNA replication and a circadian clock to anticipate changes between day and night. In some cases, these two rhythmic systems are known to be coupled by specific, cross-regulatory…
The influence of time delay in systems of two coupled excitable neurons is studied in the framework of the FitzHugh-Nagumo model. Time-delay can occur in the coupling between neurons or in a self-feedback loop. The stochastic…
We consider two identical oscillators with weak, time delayed coupling. We start with a general system of delay differential equations then reduce it to a phase model. With the assumption of large time delay, the resulting phase model has…
We have identified the existence of globally clustered chimera states in delay coupled oscillator populations and find that these states can breathe periodically, aperiodically and become unstable depending upon the value of coupling delay.…
The development of new techniques to quantitatively measure gene expression in cells has shed light on a number of systems that display oscillations in protein concentration. Here we review the different mechanisms which can produce…
Previously we showed how delay communication between globally coupled self-propelled agents causes new spatio-temporal patterns to arise when the delay coupling is fixed among all agents \cite{Forgoston08}. In this paper, we show how…
We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables…
In principle, while coupled limit cycle oscillators can overcome mismatch in intrinsic rates and match their frequencies, but zero phase lag synchronization is just achievable in the limit of zero mismatch, i.e., with identical oscillators.…
We examine the dynamics of an ensemble of phase oscillators that are divided in $k$ sets, with time-delayed coupling interactions {\em only} between oscillators in different sets or partitions. The network of interactions thus form a…
Synchronization in networks with delayed coupling are ubiquitous in nature and play a key role in almost all fields of science including physics, biology, ecology, climatology and sociology. In general, the published works on network…
We introduce an analytical approach that allows predictions and mechanistic insights into the dynamics of nonlinear oscillator networks with heterogeneous time delays. We demonstrate that time delays shape the spectrum of a matrix…
The novel idea presented in this paper is to interweave distributed model predictive control with a reliable scheduling of the information that is interchanged between local controllers of the plant subsystems. To this end, a dynamic model…
Biological neural networks exist in physical space where distance influences communication delays: a fundamental coupling between space and time absent in most artificial neural networks. While recent work has separately explored spatial…
We investigate a densely packed, non-random arrangement of forty-six chromosomes (46,XY) in human nuclei. Here, we model systems-level chromosomal crosstalk by unifying intrinsic parameters (chromosomal length and number of genes) across…
Models of misfolded proteins (MP) aim at discovering the bio-mechanical propagation properties of neurological diseases (ND) by identifying plausible associated dynamical systems. Solving these systems along the full disease trajectory is…
Spatiotemporal graph represents a crucial data structure where the nodes and edges are embedded in a geometric space and can evolve dynamically over time. Nowadays, spatiotemporal graph data is becoming increasingly popular and important,…
Existence of a new type of oscillating synchronization that oscillates between three different types of synchronizations (anticipatory, complete and lag synchronizations) is identified in unidirectionally coupled nonlinear time-delay…