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The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
We study the oscillations of neutrinos in a model in which the neutrino is coupled to a localized, idealized source and detector. By varying the spatial and temporal resolution of the source and detector we are able to model the full range…
Proposed to study the dynamics of physiological systems in which the evolution depends on the state in a previous time, the Mackey-Glass model exhibits a rich variety of behaviors including periodic or chaotic solutions in vast regions of…
Pancreatic $\beta-$cells regulate insulin secretion through complex oscillations, which are vital for glucose control and diabetes research. In this paper, an existing mathematical model of $\beta-$cell dynamics is analyzed using a…
We study the effects of nonzero time delays in stochastic synchronization problems with linear couplings in complex networks. We consider two types of time delays: transmission delays between interacting nodes and local delays at each node…
We study the robustness and stability of the yeast cell regulatory network by using a general inhomogeneous discrete model. We find that inhomogeneity, on average, enhances the stability of the biggest attractor of the dynamics and that the…
This research addresses the problem of adaptive modeling in time-series data streams with clear input-output relationships. This problem is challenging because rapid system changes (regime shifts) caused by environmental factors or input…
Self-excited systems arise in many applications, such as biochemical systems, mechanical systems with fluid-structure interaction, and fuel-driven systems with combustion dynamics. This paper presents a Lur'e model that exhibits biased…
Delay differential equations (DDEs) are widely used in mathematical modeling to describe physical and biological systems. Delays can impact model dynamics, resulting in oscillatory behavior. In physiological systems, this instability may…
We investigate the oscillatory dynamics and bifurcation structure of a reaction-diffusion system with bistable nonlinearity and mass conservation, which was proposed by [Otsuji et al, PLoS Comp. Biol. 3 (2007), e108]. The system is a useful…
Using the classical tools of nonlinear dynamics, we study the process of self-organization and the appearance of the chaos in the metabolic process in a cell with the help of a mathematical model of the transformation of steroids by a cell…
We investigate the consequences of periodic, on-off glucose infusion on the glucose-insulin regulatory system on the basis of a system-level mathematical model with two explicit time delays. Studying the effects of such infusion protocols…
This paper addresses the estimation of fractional delay and Doppler shifts in multipath channels that cause doubly selective fading-an essential task for integrated sensing and communication (ISAC) systems in high-mobility environments.…
A variety of oscillations are observed in pancreatic islets.We establish a model, incorporating two oscillatory systems of different time scales: One is the well-known bursting model in pancreatic beta-cells and the other is the…
This thesis addresses the question of stability of systems defined by differential equations which contain nonlinearity and delay. In particular, we analyze the stability of a well-known delayed nonlinear implementation of a certain…
We study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single Hopf bifurcation oscillator. Our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips,…
Discrete-time models are very convenient to simulate a nonlinear system on a computer. In order to build the discrete-time simulation models for the nonlinear feedback systems (which is a very important class of systems in many…
Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed. Mathematical modeling of biological systems with delays is usually based on Delay Differential Equations (DDEs), a kind…
The frequencies and phases of emission from extra-solar sources measured by Earth-bound observers are modulated by the motions of the observer with respect to the source, and through relativistic effects. These modulations depend critically…
We revisit the dynamics of a gene repressed by its own protein in the case where the transcription rate does not adapt instantaneously to protein concentration but is a dynamical variable. We derive analytical criteria for the appearance of…