On the Weighted Pseudo Almost Periodic Solutions of Nicholson’s Blowflies Equation

This study is concerned with the existence, uniqueness and global exponential stability of weighted pseudo almost periodic solutions of a generalized Nicholson’s blowflies equation with mixed delays. Using some differential inequalities and a fixed point theorem, sufficient conditions were obtained for the existence, uniqueness of at the least a weighted pseudo almost periodic solutions and global exponential stability of this solution. The results of this study are new and complementary to the previous ones can be found in the literature. At the end of the study an example is given to show the accuracy of our results

Lur’e Postnikov Lyapunov functional technique to global Mittag-Leffler stability of fractional-order neural networks with piecewise constant argument

International audienc

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

International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts

The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days). Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering, industry, and technology, to discuss the development of new mathematical models, theories, and applications that contribute to the advancement of scientific knowledge and practice. Authors proposed research in topics including partial and ordinary differential equations, integer and fractional order equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, probability, computational mathematics, amongst others. The conference was designed to maximize the involvement of all participants and will present the state-of- the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio

The mathematical model of Schizosaccharomyces pombe : Batch and repeated batch simulations.

Mathematical models are playing an important part in the current developments in engineering, science and biotechnology. Within this field the most fashionable and representative organisms are the ones who are genetically and physiologically tractable. Since the fission yeast Schizosaccharomyces pombe plays a role model among them and its behaviour has medical, genetic and industrial links (related to cancer research, metabolic pathways and beer production), this makes it a particularly interesting organism for study. This dissertation presents the first physiological model ever developed for the yeast S. pombe. The model allows for the simulation and prediction of batch and repeated batch experiments which are an important engineering tool in terms of optimization of industrial processes improving yield in bioreactors by predicting precise values of harvest fraction (HF) and dilution cycle times (DCT). The model has been developed within the generic modelling framework of CelCyMUS (Cell Cycle Model University of Surrey). As part of the research being carried out CelCyMUS has been up-dated by introducing the new Fortran 95 features and utilities in order to exploit its powerful new features and to keep the generic model in pace with technological software advancements. The model is a one-dimensional age-based population balance for the fission yeast S. pombe. It includes the four typical phases (S, G2, M and G1) with the G2 phase divided into two phases (G2A, G2B) and two checkpoints that govern the movement of cells between G1 and S, and G2B and M phases. The transitions (movement of cells between phases) are determined by a probability function related to the consumption of glucose. The G2B-M transition is also dependent on cell size, but since individual growth of cells is related to the consumption of the carbon source (in this case glucose), cell size is dependent upon the amount of glucose consumed per cell. The model also includes a phase for cells facing starvation before going into a meiotic cycle, with some chance of coming back to the mitotic cycle, and a death phase that accounts for cells dying with no chance of recovering at all. Parameters in the S. pombe model have been gathered from experimental data in batch culture reported in literature. Data generated from this specific model have been compared with data from experiments (Fotuhi, 2002) in batch and repeated batch cultures of S. pombe following the behaviour of population balance, consumption of nutrients, and production of metabolites. The new code was tested by successftilly reproducing data from mm-321 hybridoma cell line, the first specific model of a cell line developed in CelCyMUS. As a new feature a model of mass transfer has been incorporated in the generic framework. This mass transfer module accounts for interactions of metabolites (oxygen and carbon dioxide) in the gas and liquid phase of bioreactors. The new S. pombe model was fitted to the experiments of Creanor (1992) on synchronised cultures where the consumption of oxygen was being measured. Such experiments identify two points (G2B and G1) where the rate of oxygen uptake increased in the cycle, doubling the consumption at the end of every cycle. With the model fitted to experimental results in synchronised cultures of S. pombe the model was then used to simulate desynchronised cultures. S. pombe was successfully tested when reproducing experimental data generated by Fotuhi (2002) in S.pombe for batch and repeated batch bioreactors. The S. pombe model was able to simulate cell number, oxygen and glucose consumption. Carbon dioxide and ATP production were predicted by the model however there was no experimental data to compare with. Now that the S. pombe model has been tested against experimental data it will be applied in a model-based observer strategy for the online control of bioreactors