We consider a mathematical model describing the maturation process of stem cells up to fully mature cells. The model is formulated as a differential equation with state-dependent delay, where maturity is described as a continuous variable. The maturation rate of cells may be regulated by the amount of mature cells and, moreover, it may depend on cell maturity: we investigate how the stability of equilibria is affected by the choice of the maturation rate. We show that the principle of linearised stability holds for this model, and develop some analytical methods for the investigation of characteristic equations for fixed delays. For a general maturation rate we resort to numerical methods and we extend the pseudospectral discretisation technique to approximate the state-dependent delay equation with a system of ordinary differential equations. This is the first application of the technique to nonlinear state-dependent delay equations, and currently the only method available for studying the stability of equilibria by means of established software packages for bifurcation analysis. The numerical method is validated on some cases when the maturation rate is independent of maturity and the model can be reformulated as a fixed-delay equation via a suitable time transformation. We exploit the analytical and numerical methods to investigate the stability boundary in parameter planes. Our study shows some drastic qualitative changes in the stability boundary under assumptions on the model parameters, which may have important biological implications.
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http://dx.doi.org/10.1007/s00285-019-01357-0 | DOI Listing |
ISA Trans
December 2024
Department of Applied Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada. Electronic address:
This article studies the problem of formation tracking control in multi-agent systems, achieved in finite time, under challenging conditions such as strong nonlinearity, aperiodic intermittent communication, and time-delay effects, all within a hybrid impulsive framework. The impulses are categorized as either stabilizing control impulses or disruptive impulses. Furthermore, by integrating Lyapunov-based stability theory, graph theory, and the linear matrix inequality (LMI) method, new stability criteria are established.
View Article and Find Full Text PDFBrain
November 2024
Department of Physiology and Neuroscience Program, Biomedicine Discovery Institute, Monash University, Clayton, VIC 3800, Australia.
ISA Trans
October 2024
College of Navigation, Dalian Maritime University, Dalian 116026, People's Republic of China; School of Automation Engineering, University of Electronic Science, and Technology of China, Chengdu 611731, People's Republic of China. Electronic address:
This paper presents the design of a Lyapunov matrix-based adaptive resilient controller for unmanned marine vehicles (UMVs) under state-dependent sensor attacks, input-dependent thruster attacks, and time delays. Different from the thruster attack model that depends on state information, the thruster attack model studied in this paper is related to control input, that is, the input-dependent thruster attacks. This implies that the designed correction signal is also affected by the attacks.
View Article and Find Full Text PDFPCN Rep
September 2024
Department of Neuropsychiatry, School of Medicine Fukushima Medical University Fukushima Japan.
Background: Cognitive abnormalities associated with electroconvulsive therapy (ECT) are limited to the first few days after treatment. Mismatch negativity (MMN) is an event-related potential that reflects an automatic auditory change detection process under nonattention conditions and cognitive function in psychotic disorders and may be trait- or state-dependent. This study aimed to report the changes in MMN and cognitive function after two ECT treatments in a female patient who underwent maintenance ECT for atypical psychosis.
View Article and Find Full Text PDFNeural Netw
November 2024
School of Sciences, University of Science and Technology Liaoning, Anshan, Liaoning 114051, China. Electronic address:
This research delves into the reachable set estimation (RSE) problem for general switched delayed neural networks (SDNNs) in the discrete-time context. Note that existing relevant research on SDNNs predominantly relies on either time-dependent or state-dependent switching approaches. The time-dependent versions necessitate the stability of each subnetwork beforehand, whereas the state-dependent switching strategies solely depend on the current state, thus disregarding the historical information of the neuron states.
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