Author
Flaviano Battelli
Bio: Flaviano Battelli is an academic researcher from Marche Polytechnic University. The author has contributed to research in topics: Homoclinic orbit & Heteroclinic orbit. The author has an hindex of 12, co-authored 58 publications receiving 8157 citations.
Papers published on a yearly basis
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Book•
01 Jan 2004
TL;DR: The fourth volume in a series of volumes devoted to self-contained and up-to-date surveys in the theory of ODEs was published by as discussed by the authors, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience.
Abstract: This handbook is the fourth volume in a series of volumes devoted to self contained and up-to-date surveys in the theory of ordinary differential equations, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience. It covers a variety of problems in ordinary differential equations. It provides pure mathematical and real world applications. It is written for mathematicians and scientists of many related fields.
7,749 citations
TL;DR: In this paper, the chaotic behavior of a time dependent perturbation of a discontinuous differential equation whose unperturbed part has a sliding homoclinic orbit that is a solution to a hyperbolic fixed point with a part belonging to a discontinuity surface is studied.
54 citations
TL;DR: In this article, the authors studied the chaotic behavior of time-perturbed discontinuous systems whose unperturbed part has a piecewise C 1 homoclinic solution transversally crossing the discontinuity manifolds.
51 citations
TL;DR: In this paper, the bifurcations of bounded solutions from homoclinic orbits for time-perturbed discontinuous systems were studied and a functional analytic method was used.
Abstract: We study bifurcations of bounded solutions from homoclinic orbits for time-perturbed discontinuous systems. Functional analytic method is used. An illustrative example of a periodically perturbed piecewise linear differential equation in $$\mathbb{R}^3$$
is presented.
47 citations
TL;DR: In this paper, the authors follow a functional analytic approach to study the chaotic behavior of time-perturbed discontinuous systems whose unperturbed part has a piecewise C 1 homoclinic solution that crosses transversally the discontinuity manifold.
Abstract: We follow a functional analytic approach to study the problem of chaotic behaviour in time-perturbed discontinuous systems whose unperturbed part has a piecewise C
1 homoclinic solution that crosses transversally the discontinuity manifold. We show that if a certain Melnikov function has a simple zero at some point, then the system has solutions that behave chaotically. Application of this result to quasi periodic systems are also given.
30 citations
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TL;DR: Threshold theorems involving the basic reproduction number, the contact number, and the replacement number $R$ are reviewed for classic SIR epidemic and endemic models and results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups.
Abstract: Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number $R_{0}$, the contact number $\sigma$, and the replacement number $R$ are reviewed for the classic SIR epidemic and endemic models. Similar results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups. Values of $R_{0}$ and $\sigma$ are estimated for various diseases including measles in Niger and pertussis in the United States. Previous models with age structure, heterogeneity, and spatial structure are surveyed.
5,915 citations
TL;DR: This paper analyses the stability and fairness of two classes of rate control algorithm for communication networks, which provide natural generalisations to large-scale networks of simple additive increase/multiplicative decrease schemes, and are shown to be stable about a system optimum characterised by a proportional fairness criterion.
Abstract: This paper analyses the stability and fairness of two classes of rate control algorithm for communication networks. The algorithms provide natural generalisations to large-scale networks of simple additive increase/multiplicative decrease schemes, and are shown to be stable about a system optimum characterised by a proportional fairness criterion. Stability is established by showing that, with an appropriate formulation of the overall optimisation problem, the network's implicit objective function provides a Lyapunov function for the dynamical system defined by the rate control algorithm. The network's optimisation problem may be cast in primal or dual form: this leads naturally to two classes of algorithm, which may be interpreted in terms of either congestion indication feedback signals or explicit rates based on shadow prices. Both classes of algorithm may be generalised to include routing control, and provide natural implementations of proportionally fair pricing.
5,566 citations
TL;DR: This study indicates that SyN, with cross-correlation, is a reliable method for normalizing and making anatomical measurements in volumetric MRI of patients and at-risk elderly individuals.
4,233 citations
TL;DR: It is shown that the regularity properties of the Lyapunov function and those of the settling-time function are related and converse Lyap Unov results can only assure the existence of continuous Lyap unov functions.
Abstract: Finite-time stability is defined for equilibria of continuous but non-Lipschitzian autonomous systems. Continuity, Lipschitz continuity, and Holder continuity of the settling-time function are studied and illustrated with several examples. Lyapunov and converse Lyapunov results involving scalar differential inequalities are given for finite-time stability. It is shown that the regularity properties of the Lyapunov function and those of the settling-time function are related. Consequently, converse Lyapunov results can only assure the existence of continuous Lyapunov functions. Finally, the sensitivity of finite-time-stable systems to perturbations is investigated.
3,894 citations
TL;DR: This is the first study to use a consistent transformation framework to provide a reproducible evaluation of the isolated effect of the similarity metric on optimal template construction and brain labeling, and to quantify the similarity of templates derived from different subgroups.
3,491 citations