510 research outputs found
Effect of state-dependent time delay on dynamics of trimming of thin walled structures
Acknowledgments This work was supported by the National Key R&D Program of China (2020YFA0714900), National Natural Science Foundation of China (52075205, 92160207, 52090054, 52188102).Peer reviewedPostprin
Recommended from our members
Control of mosaic disease using microbial biostimulants: insights from mathematical modelling
A major challenge to successful crop production comes from viral diseases of plants that cause significant crop losses, threatening global food security and the livelihoods of countries that rely on those crops for their staple foods or source of income. One example of such diseases is a mosaic disease of plants, which is caused by begomoviruses and is spread to plants by whitefly. In order to mitigate negative impact of mosaic disease, several different strategies have been employed over the years, including roguing/replanting of plants, as well as using pesticides, which have recently been shown to be potentially dangerous to the environment and humans. In this paper we derive and analyse a mathematical model for control of mosaic disease using natural microbial biostimulants that, besides improving plant growth, protect plants against infection through a mechanism of RNA interference. By analysing the stability of the system’s steady states, we will show how properties of biostimulants affect disease dynamics, and in particular, how they determine whether the mosaic disease is eradicated or is rather maintained at some steady level. We will also present the results of numerical simulations that illustrate the behaviour of the model in different dynamical regimes, and discuss biological implications of theoretical results for the practical purpose of control of mosaic disease
bifurcation analysis of a delayed worm propagation model with saturated incidence
This paper is concerned with a delayed SVEIR worm propagation model with saturated incidence. The main objective is to investigate the effect of the time delay on the model. Sufficient conditions for local stability of the positive equilibrium and existence of a Hopf bifurcation are obtained by choosing the time delay as the bifurcation parameter. Particularly, explicit formulas determining direction of the Hopf bifurcation and stability of the bifurcating periodic solutions are derived by using the normal form theory and the center manifold theorem. Numerical simulations for a set of parameter values are carried out to illustrate the analytical results
Multiobjective nonfragile fuzzy control for nonlinear stochastic financial systems with mixed time delays
In this study, a multiobjective nonfragile control is proposed for a class of stochastic Takagi and Sugeno (T–S) fuzzy systems with mixed time delays to guarantee the optimal H2 and H∞ performance simultaneously. Firstly, based on the T–S fuzzy model, two form of nonfragile state feedback controllers are designed to stabilize the T–S fuzzy system, that is to say, nonfragile state feedback controllers minimize the H2 and H∞ performance simultaneously. Then, by applying T–S fuzzy approach, the multiobjective H2/H∞ nonfragile fuzzy control problem is transformed into linear matrix inequality (LMI)-constrained multiobjective problem (MOP). In addition, we efficiently solve Pareto optimal solutions for the MOP by employing LMI-based multiobjective evolution algorithm (MOEA). Finally, the validity of this approach is illustrated by a realistic design example
Pattern formation and bifurcation analysis of delay induced fractional-order epidemic spreading on networks
The spontaneous emergence of ordered structures, known as Turing patterns, in
complex networks is a phenomenon that holds potential applications across
diverse scientific fields, including biology, chemistry, and physics. Here, we
present a novel delayed fractional-order
susceptible-infected-recovered-susceptible (SIRS) reaction-diffusion model
functioning on a network, which is typically used to simulate disease
transmission but can also model rumor propagation in social contexts. Our
theoretical analysis establishes the Turing instability resulting from delay,
and we support our conclusions through numerical experiments. We identify the
unique impacts of delay, average network degree, and diffusion rate on pattern
formation. The primary outcomes of our study are: (i) Delays cause system
instability, mainly evidenced by periodic temporal fluctuations; (ii) The
average network degree produces periodic oscillatory states in uneven spatial
distributions; (iii) The combined influence of diffusion rate and delay results
in irregular oscillations in both time and space. However, we also find that
fractional-order can suppress the formation of spatiotemporal patterns. These
findings are crucial for comprehending the impact of network structure on the
dynamics of fractional-order systems.Comment: 23 pages, 9 figure
Mean field modelling of human EEG: application to epilepsy
Aggregated electrical activity from brain regions recorded via an electroencephalogram (EEG),
reveal that the brain is never at rest, producing a spectrum of ongoing oscillations that
change as a result of different behavioural states and neurological conditions. In particular,
this thesis focusses on pathological oscillations associated with absence seizures that typically
affect 2–16 year old children. Investigation of the cellular and network mechanisms for absence
seizures studies have implicated an abnormality in the cortical and thalamic activity in the
generation of absence seizures, which have provided much insight to the potential cause of this
disease. A number of competing hypotheses have been suggested, however the precise cause
has yet to be determined. This work attempts to provide an explanation of these abnormal
rhythms by considering a physiologically based, macroscopic continuum mean-field model of
the brain's electrical activity. The methodology taken in this thesis is to assume that many
of the physiological details of the involved brain structures can be aggregated into continuum
state variables and parameters. The methodology has the advantage to indirectly encapsulate
into state variables and parameters, many known physiological mechanisms underlying the
genesis of epilepsy, which permits a reduction of the complexity of the problem. That is, a
macroscopic description of the involved brain structures involved in epilepsy is taken and then
by scanning the parameters of the model, identification of state changes in the system are
made possible. Thus, this work demonstrates how changes in brain state as determined in
EEG can be understood via dynamical state changes in the model providing an explanation
of absence seizures. Furthermore, key observations from both the model and EEG data
motivates a number of model reductions. These reductions provide approximate solutions of
seizure oscillations and a better understanding of periodic oscillations arising from the involved
brain regions. Local analysis of oscillations are performed by employing dynamical systems
theory which provide necessary and sufficient conditions for their appearance. Finally local
and global stability is then proved for the reduced model, for a reduced region in the parameter
space. The results obtained in this thesis can be extended and suggestions are provided for
future progress in this area
The role of mRNA and protein stability in the function of coupled positive and negative feedback systems in eukaryotic cells
Oscillators and switches are important elements of regulation in biological systems. These are composed of coupling negative feedback loops, which cause oscillations when delayed, and positive feedback loops, which lead to memory formation. Here, we examine the behavior of a coupled feedback system, the Negative Autoregulated Frustrated bistability motif (NAF). This motif is a combination of two previously explored motifs, the frustrated bistability motif (FBM) and the negative auto regulation motif (NAR), which both can produce oscillations. The NAF motif was previously suggested to govern long term memory formation in animals, and was used as a synthetic oscillator in bacteria. We build a mathematical model to analyze the dynamics of the NAF motif. We show analytically that the NAF motif requires an asymmetry in the strengths of activation and repression links in order to produce oscillations. We show that the effect of time delays in eukaryotic cells, originating from mRNA export and protein import, are negligible in this system. Based on the reported protein and mRNA half-lives in eukaryotic cells, we find that even though the NAF motif possesses the ability for oscillations, it mostly promotes constant protein expression at the biologically relevant parameter regimes
A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis
The aim of this paper is to explain critical features of the human primary generalized
epilepsies by investigating the dynamical bifurcations of a nonlinear model of the
brain’s mean field dynamics. The model treats the cortex as a medium for the
propagation of waves of electrical activity, incorporating key physiological processes
such as propagation delays, membrane physiology and corticothalamic feedback.
Previous analyses have demonstrated its descriptive validity in a wide range of
healthy states and yielded specific predictions with regards to seizure phenomena. We
show that mapping the structure of the nonlinear bifurcation set predicts a number of
crucial dynamic processes, including the onset of periodic and chaotic dynamics as
well as multistability. Quantitative study of electrophysiological data supports the
validity of these predictions and reveals processes unique to the global bifurcation set.
Specifically, we argue that the core electrophysiological and cognitive differences
between tonic-clonic and absence seizures are predicted by the global bifurcation
diagram of the model’s dynamics. The present study is the first to present a unifying
explanation of these generalized seizures using the bifurcation analysis of a dynamical
model of the brain
- …