Controllability of impulsive hybrid integro-differential systems

Sivasundaram, S.; Uvah, Josaphat

doi:10.1016/j.nahs.2008.04.003

Cited by 16 publications

(5 citation statements)

References 6 publications

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“…The topic of the mathematical control is an important issue considering the importance of optimizing protocols of vaccination and drug application. The introduction of mathematical control has been considered for ODE-based models [26][27][28], PDE-based models, including integro-differential equations [29][30][31]. The equations of fractional order are suggested by Kostić [9] as a new tool for the modeling of complex systems and specifically for physiological and pathological fibrosis.…”

Section: Mathematical Methods Towards a Multiscale Modelmentioning

confidence: 99%

Multiscale modeling of fibrosis – What's next? Reply to Comments on “Towards a unified approach in the modeling of fibrosis: A review with research perspective” by Martine Ben Amar and Carlo Bianca

Amar

Bianca

2016

Physics of Life Reviews

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Section: Mathematical Methods Towards a Multiscale Modelmentioning

confidence: 99%

Multiscale modeling of fibrosis – What's next? Reply to Comments on “Towards a unified approach in the modeling of fibrosis: A review with research perspective” by Martine Ben Amar and Carlo Bianca

Amar

Bianca

2016

Physics of Life Reviews

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“…The mathematical control of ODE-based models is much developed, see the book [49]. Recently many contributions have been addressed to the control and optimization of PDE-based models, including integrodifferential equations, see, among others [5,45] and the references cited therein. In particular, the thermostatted kinetic theory approach is based on the definition of an external force field whose action can modify the asymptotic behavior of the system.…”

Section: Critical Analysis and Research Perspectivesmentioning

confidence: 99%

Modeling the antigen recognition by B-cell and T-cell receptors through thermostatted kinetic theory methods

Bianca

Brézin

2017

Int. J. Biomath.

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The activation and the resulting response of the immune system to antigens comprise different complex processes and cells. This paper aims at modeling the processes of recognition and learning of the immune system by means of the thermostatted kinetic theory methods. Specifically, the thermostatted kinetic framework is firstly generalized for taking into account that in some processes of proliferation of the cells, the rate is also function of the degree of information exchanged amongst cells. In particular, within the new framework, a mathematical model is proposed for miming the recognition process of the immune system through the definition of interactions between the cytotoxic and humoral components of the adaptive immune system via T-and B-cells. The model validation is obtained by performing a sensitivity analysis on the parameters which depicts the main emerging phenomena and the different phases of the recognition and learning of the immune system.

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“…The authors of [61] investigated the complete controllability of hybrid impulsive integrodifferential systems. In papers [62,63] the necessary and sufficient conditions for state controllability and observability for a class of linear time-varying impulsive systems were considered.…”

Section: Introductionmentioning

confidence: 99%

Banach fixed-point theorem in semilinear controllability problems – a survey

Klamka

Babiarz

Niezabitowski

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. The main aim of this article is to review the existing state of art concerning the complete controllability of semilinear dynamical systems. The study focus on obtaining the sufficient conditions for the complete controllability for various systems using the Banach fixedpoint theorem. We describe the results for stochastic semilinear functional integro-differential system, stochastic partial differential equations with finite delays, semilinear functional equations, a stochastic semilinear system, a impulsive stochastic integro-differential system, semilinear stochastic impulsive systems, an impulsive neutral functional evolution integro-differential system and a nonlinear stochastic neutral impulsive system. Finally, two examples are presented.

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Controllability of impulsive hybrid integro-differential systems

Cited by 16 publications

References 6 publications

Multiscale modeling of fibrosis – What's next? Reply to Comments on “Towards a unified approach in the modeling of fibrosis: A review with research perspective” by Martine Ben Amar and Carlo Bianca

Multiscale modeling of fibrosis – What's next? Reply to Comments on “Towards a unified approach in the modeling of fibrosis: A review with research perspective” by Martine Ben Amar and Carlo Bianca

Modeling the antigen recognition by B-cell and T-cell receptors through thermostatted kinetic theory methods

Banach fixed-point theorem in semilinear controllability problems – a survey

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