Stability in Terms of Two Measures for Nonlinear Impulsive Systems on Time Scales

We investigate some stability problems in terms of two measures for nonlinear dynamic systems on time scales with fixed moments of impulsive effects. Sufficient conditions for (uniform) stability, (uniform) asymptotic stability, and instability in terms of two measures are derived by using the method of Lyapunov functions. Our results include the existing results as special cases when the time scale reduces to the set of real numbers. Particularly, our results provide stability criteria for impulsive discrete systems in terms of two measures, which have not been investigated extensively. Two examples are presented to illustrate the efficiency of the proposed results

Stability in Terms of Two Measures for Nonlinear Impulsive Systems on Time Scales

We investigate some stability problems in terms of two measures for nonlinear dynamic systems on time scales with fixed moments of impulsive effects. Sufficient conditions for (uniform) stability, (uniform) asymptotic stability, and instability in terms of two measures are derived by using the method of Lyapunov functions. Our results include the existing results as special cases when the time scale reduces to the set of real numbers. Particularly, our results provide stability criteria for impulsive discrete systems in terms of two measures, which have not been investigated extensively. Two examples are presented to illustrate the efficiency of the proposed results

Invariant manifold theory for impulsive functional differential equations with applications

The primary contribution of this thesis is a development of invariant manifold theory for impulsive functional differential equations. We begin with an in-depth analysis of linear systems, immersed in a nonautonomous dynamical systems framework. We prove a variation-of-constants formula, introduce appropriate generalizations of stable, centre and unstable subspaces, and develop a Floquet theory for periodic systems. Using the Lyapunov-Perron method, we prove the existence of local centre manifolds at a nonhyperbolic equilibrium of nonlinear impulsive functional differential equations. Using a formal differentiation procedure in conjunction with machinery from functional analysis -- specifically, contraction mappings on scales of Banach spaces -- we prove that the centre manifold is smooth in the state space. By introducing a coordinate system, we are able to prove that the coefficients of any Taylor expansion of the local centre manifold are unique and sufficiently regular in the time and lag arguments that they can be computed by solving an impulsive boundary-value problem. After proving a reduction principle, this leads naturally to explorations into bifurcation theory, where we establish generalizations of the classical fold and Hopf bifurcations for impulsive delay differential equations. Aside from the centre manifold, we demonstrate the existence and smoothness of stable and unstable manifolds and prove a linearized stability theorem. One of the applications of the theory above is an analysis of a SIR model with pulsed vaccination and finite temporary immunity modeled by a discrete delay. We determine an analytical stability criteria for the disease-free equilibrium and prove the existence of a transcritical bifurcation of periodic solutions at some critical vaccination coverage level for generic system parameters. Then, using numerical continuation and a monodromy operator discretization scheme, we track the bifurcating endemic periodic solution until a Hopf point is identifed. A cylinder bifurcation is observed; the periodic orbit expands into a cylinder in the extended phase space before eventually contracting onto a periodic orbit as the vaccination coverage vanishes. The other application is an impulsive stabilization method based on centre manifold reduction and optimization principles. Assuming a cost structure on the impulsive controller and a desired convergence rate target, we prove that under certain conditions there is always an impulsive controller that can stabilize a nonhyperbolic equilibrium with a trivial unstable subspace, robustly with respect to parameter perturbation, while guaranteeing a minimal cost. We then exploit the low-dimensionality of the centre manifold to develop a two-stage program that can be implemented to compute the optimal controller. To demonstrate the effectiveness of the two-stage program, which we call the centre probe method, we use the method to stabilize a complex network of 100 diffusively coupled nodes at a Hopf point. The cost structure is one that assigns higher cost to controlling of nodes that have more neighbours, while the jump functionals are required to be diagonal -- that is, they do not introduce further coupling. We also introduce a secondary goal, which is that the number of nodes that are controlled is minimized

Avionic air data sensors fault detection and isolation by means of singular perturbation and geometric approach

Singular Perturbations represent an advantageous theory to deal with systems characterized by a two-time scale separation, such as the longitudinal dynamics of aircraft which are called phugoid and short period. In this work, the combination of the NonLinear Geometric Approach and the Singular Perturbations leads to an innovative Fault Detection and Isolation system dedicated to the isolation of faults affecting the air data system of a general aviation aircraft. The isolation capabilities, obtained by means of the approach proposed in this work, allow for the solution of a fault isolation problem otherwise not solvable by means of standard geometric techniques. Extensive Monte-Carlo simulations, exploiting a high fidelity aircraft simulator, show the effectiveness of the proposed Fault Detection and Isolation system.Singular Perturbations represent an advantageous theory to deal with systems characterized by a two-time scale separation, such as the longitudinal dynamics of aircraft which are called phugoid and short period. In this work, the combination of the NonLinear Geometric Approach and the Singular Perturbations leads to an innovative Fault Detection and Isolation system dedicated to the isolation of faults affecting the air data system of a general aviation aircraft. The isolation capabilities, obtained by means of the approach proposed in this work, allow for the solution of a fault isolation problem otherwise not solvable by means of standard geometric techniques. Extensive Monte-Carlo simulations, exploiting a high fidelity aircraft simulator, show the effectiveness of the proposed Fault Detection and Isolation system

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

Abstract book

Welcome at the International Conference on Differential and Difference Equations & Applications 2015. The main aim of this conference is to promote, encourage, cooperate, and bring together researchers in the fields of differential and difference equations. All areas of differential & difference equations will be represented with special emphasis on applications. It will be mathematically enriching and socially exciting event. List of registered participants consists of 169 persons from 45 countries. The five-day scientific program runs from May 18 (Monday) till May 22, 2015 (Friday). It consists of invited lectures (plenary lectures and invited lectures in sections) and contributed talks in the following areas: Ordinary differential equations, Partial differential equations, Numerical methods and applications, other topics

Riskeeriv käitumine: seosed isiksuse ja pärilikkusega ning sekkumine vigastuste ennetamiseks

Väitekirja elektrooniline versioon ei sisalda publikatsiooneVigastussurmad on oluliselt seotud riskeeriva käitumisega, mida mõjutavad mitmed isiksuslikud (nt impulsiivsus) tegurid on suuresti pärilikud. Impulsiivne käitumine on seotud nii serotoniini- kui ka dopamiinisüsteemi toimimisega. Väitekirja peamisteks eesmärkideks oli selgitada 1) riskeeriva käitumise seoseid isiklike ja isiksuslike tegurite ning serotoniini- ja dopamiinisüsteemi markeritega ning 2) kas riskeeriva käitumise ennetamiseks läbiviidud sekkumine, mis on osutunud efektiivseks, on efektiivne ka siis kui seda viivad läbi autokoolide õpetajad. Kuna riskeeriv käitumine ning seda mõjutavad tegurid erinevad teismeliseeas ja täiskasvanuks saades, siis kasutati väitekirjas kolme erinevat valimit: kuuendate klasside õpilased (n=699), kordusmõõtmistes osalenud 15-18 aastased õpilased (n=483) ning autokoolide õpilased (n=1441). Tulemustest ilmnes, et riskide võtmine on seotud tugevamini teatud isiksuslike teguritega (nt impulsiivsus, ekstravertsus, tahteline kontroll) ning dopamiinisüsteemi kõrgema ja serotoniinisüsteemi madalama aktiivsusega, aga ka teadmiste ja oskustega. Tulemustest saadi kinnitust, et lühikese psühholoogilise sekkumisega on võimalik vähendada riskikäitumist. Sekkumise efektiivsus tõestas, et riskeeriva käitumisega seotud isiksuse ja bioloogilisi riskitegureid tundes on võimalik koolis neid teemasid õpetajate poolt käsitleda nii, et viia riskikäitumise ennetustööd läbi efektiivselt. Lisaks ohtudega seotud teadmistele on vaja harjutada ja läbi mängida erinevaid situatsioone, et suurendada teadvustatud käitumise rolli otsustusprotsessis ning vähendada seeläbi teadvustamata ja impulsiivse otsustamise mõju. Lisaks tehniliste oskuste arendamisele (nt jalgratta või auto juhtimine, lõkke tegemine, ujumisoskus) on vajalik arendada nende tegevustega seotud ohutusalaseid (situatsioonist tulenevate ohtude hindamine) ja sotsiaalseid (nt enesekontroll, teistega arvestamine) oskuseidInjury deaths are often caused by risk-taking behaviour that in turn is associated with several personality factors (e.g., impulsivity) that are to a large degree heritable. Impulsive behaviour is strongly related to the functioning of both serotonin and dopamine systems. The main aims of this thesis were to find out 1) links between risk-taking behaviour and personality factors and markers of the function of the serotonin and dopamine systems, and 2) whether a previously used brief intervention to prevent risk-taking behaviour is still successful if conducted by driving school teachers. Since risk-taking behaviour and the factors influencing it can differ in teenager and adult age, three different samples were used: sixth grade students (n=699), 15-18-year-old students who participated in the longitudinal study (n=483) and driving school students (n=1441). The results revealed that risk-taking has significant links with certain personality traits (e.g., impulsivity, extraversion, effortful control), higher activity of the dopamine system and lower activity of the serotonin system, but also with knowledge and skills. The results confirmed that the brief psychological intervention helps to reduce risk-taking behaviour. The efficiency of the intervention suggests that if the personal and biological factors causing risk-taking behaviour are known, teachers can deal with them. In addition to the knowledge of dangers, different situations need to be practiced and played through to increase the role of conscious behaviour in the decision-making process, and therefore to decrease the influence of unconscious and impulsive decision-making. In addition to the development of technical skills (e.g., riding a bike, driving a car, making fire, swimming), there is also a need to develop safety-related (evaluation of situation-related dangers) and social skills (e.g., self-control, consideration of others) associated with this activity.https://www.ester.ee/record=b536212