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240 results on '"Dercole, Fabio"'

54. SlideCont: an Aauto97 driver for bifurcation analysis of Filippov systems

Author

Dercole, Fabio and Kuznetsov, Yuri A.

Subjects
Algorithm, Differential equations -- Research, Algorithms -- Research
Abstract

SLIDECONT, an AUTO97 driver for sliding bifurcation analysis of discontinuous piecewise-smooth autonomous systems, known as Filippov systems, is described in detail. Sliding bifurcations are those in which some sliding on the discontinuity boundary is critically involved. The software allows for detection and continuation of codimension-1 sliding bifurcations as well as detection of some codimension-2 singularities, with special attention to planar systems (n = 2). Some bifurcations are also supported for n-dimensional systems. This article gives a brief introduction to Filippov systems, describes the structure of SLIDECONT and all computations supported by SLIDECONT 2.0. Several examples, which are distributed together with the source code of SLIDECONT, are presented. Categories and Subject Descriptors: G.1.7 [Numerical Analysis]: Ordinary Differential Equations--Boundary value problems; G.1.0 [Numerical Analysis]: General--Numerical algorithms; J.2 [Physical Sciences and Engineering]; J.3 [Life and Medical Sciences] General Terms: Algorithms Additional Key Words and Phrases: AUTO97, numerical continuation, piecewise-smooth differential equations, Filippov systems, sliding bifurcations

Published
2005

61. Adaptive dynamics and technological change

Author

Dercole, Fabio, Dieckmann, Ulf, Obersteiner, Michael, and Rinaldi, Sergio

Subjects
Technological innovations -- Evaluation, Product development -- Methods, Adaptive control, Time to market, Business, Business, general, High technology industry
Abstract

This paper is about the emergence of technological variety arising from market interaction and technological innovation. Existing products in the market compete with innovative ones resulting in a slow and continuous evolution of the underlying technological characteristics of successful products. When technological evolution reaches an equilibrium, it can either be an evolutionarily stable strategy (ESS), where marginally innovative products do not penetrate the market, or a branching point, where new products coexist along with established ones. Thus, technological branching can give rise to product variety. In the paper we first introduce adaptive dynamics (AD), a recently proposed theory of evolutionary processes, aiming at modeling various features of technological change. By separating the timescale typical of market competition processes from that on which marginal innovations drive technological change, AD formally describes products coevolution by means of ordinary differential equations. Then, a first application of AD in economics is presented and discussed in detail. The problem we discuss is intentionally very simple, in order to clearly exemplify all the steps of the analysis, but allows to draw the following intuitive conclusion: product variety is expected in market sectors characterized by a wide capacity to absorb different technologies and by competition-safe niches even for relatively similar products. The limitations of the AD approach, as well as some promising further applications in economics and social sciences, are briefly discussed at the concluding section. Keywords: Adaptive dynamics; Market dynamics; Innovation dynamics; Characteristic trait; Technological branching; Product variety

Published
2008

75. Modeling Love Dynamics

Author

Rinaldi, Sergio, primary, Rossa, Fabio Della, additional, Dercole, Fabio, additional, Gragnani, Alessandra, additional, and Landi, Pietro, additional

Published
2015
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76. Numerical Bifurcation Analysis

Author

Meijer, Hil Gaétan Ellart, Dercole, Fabio, Oldeman, Bart, and Myers, R.A.

Subjects
Mathematical optimization, Dynamical systems theory, business.industry, Ode, METIS-264107, Parameter space, Type (model theory), Nonlinear system, Software, Development (topology), Bifurcation theory, Applied mathematics, IR-68369, EWI-16425, business, Mathematics
Abstract

The theory of dynamical systems studies the behavior of solutions of systems, like nonlinear ordinary differential equations (ODEs), depending upon parameters. Using qualitative methods of bifurcation theory, the behavior of the system is characterized for various parameter combinations. In particular, the catalog of system behaviors showing qualitative differences can be identified, together with the regions in parameter space where the different behaviors occur. Bifurcations delimit such regions. Symbolic and analytical approaches are in general infeasible, but numerical bifurcation analysis is a powerful tool that aids in the understanding of a nonlinear system. When computing power became widely available, algorithms for this type of analysis matured and the first codes were developed. With the development of suitable algorithms, the advancement in the qualitative theory has found its way into several software projects evolving over time. The availability of software packages allows scientists to study and adjust their models and to draw conclusions about their dynamics.

Published
2009

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