Laura Gardini / Professore Emerito

Prof. Laura Gardini <laura.gardini@uniurb.it>
Full Professor of Mathematics for Economics (1994-)
Department DESP, University of Urbino, Italy
http://www.mdef.it/laura-gardini/
http://scholar.google.it/citations?user=wjOZ4EoAAAAJ&hl=en
https://www.researchgate.net/profile/Laura-Gardini

Scopus h-index: 31

Co-Editor in Chief of the International Jpurnal MATCOM, Q1 in Applied mathematics,

https://www.journals.elsevier.com/mathematics-and-computers-in-simulation

Associate Editor of Comm. in Nonlinear Science and Numerical Simulations. from March 2019

Associate Editor of Journal of Difference Equations and Applications. from 2015

Elected Member of the Scientific Board of ISDE (International Society of Difference Equations) 2019-2021, 2021-2023

Member of the Scientific Committee of the European Conference on Iteration Theory. 1996-(elected Chief  2018-)

Elected Member of the Scientific Committee of the SICC (Italian Society of Chaos and Complexity). 2010-2022

Researches Interests

Dynamical Systems (stability, bifurcations and analysis of complex behaviors) and their applications to the modeling of the evolution in Economic, Financial, Social, Biological and Physical systems. The main results have been obtained in the anlysis of noninvertible maps of the plane, following the pioneering works of I. Gumowski and C. Mira. These tools have been improved and applied in the study of the dynamics in smooth models, piecewise-smooth and discontinuous ones.  
In particular, the recent research fields include:   

• Global properties and bifurcations of attracting sets and basins of attraction in discrete time dynamical systems: homoclinic bifurcations and contact bifurcations that change the topological structure of attractors or basins of attraction.
• Global bifurcations in iterated two-dimensional maps not defined in the whole plane due to the presence of a vanishing denominators, and related properties of focal points, prefocal curves, lobes, crescents, unbounded sets of attraction.
• Qualitative analysis of discrete dynamical systems represented by the iteration of noninvertible maps, and study of their properties and global bifurcations by the use of critical sets.
• Symmetric dynamical systems and related problems of chaos synchronization, on-off intermittency, riddling and blowout bifurcations related to the presence of Milnor attractors. Applications to dynamic symmetric games.
• Border collision bifurcations in piecewise smooth maps, continuous and discontinuous.
• Dynamic modeling in Economic, Finance and Social Sciences: dynamic oligopoly games, models of economies with boundedly rational agents (and related problems of expectations and learning schemes) models of economies with heterogeneous agents, nonlinear models of business cycle.

Author or coauthor in more than 200 publications in International Journals.

Books:

• V. Avrutin, L. Gardini, I. Sushko and F. Tramontana, “Continuous and Discontinuous Piecewise-Smooth One-Dimensional Maps: Invariant Sets and Bifurcation structures”, World Scientific, Singapore, 2019, 634 pages, https://doi.org/10.1142/8285, ISBN: 978-981-4368-82-7.
• C. Mira, L. Gardini, A. Barugola, J.C. Cathala "Chaotic Dynamics in Two-Dimensional NonivertibIe Maps", WORLD-SCIENTIFIC Publ. Co., "Nonlinear Sciences, Series A", Singapore 1996. ISBN 9810216475
• R. Abraham, L. Gardini, C. Mira "Chaos in Discrete Dynamical Systems (A visual introduction in 2 dimensions)", TELOS, SPRINGER-VERLAG, N-Y 1997. ISBN 0387943005
• G.I. Bischi, R. Carini, L. Gardini, P. Tenti "Sulle Orme del Caos. Comportamenti complessi in modelli matematici semplici" Bruno Mondadori Editore, Prima e Seconda edizione, 2004. Terza edizione 2010. ISBN 8842495913

Co-Editor in several Springer books, and Special Issues in International Journals:

• Mathematics and Computers in Simulation,
• Chaos Solitons & Fractals,
• Journal of Difference Equations and Applications,
• Communications in Nonlinear Science and Numerical Simulations,
• CHAOS an Interdisciplinary Journal
• Nonlinear Dynamics
• Journal of Economic Interaction and Coordination
• Discrete and Continuous Dynamical Systems -Series B
• Decisions in Economics and Finance

• G.I. Bischi, L. Gardini, A. Naimzada, Path dependence in models with fading memory or adaptive learning, in G.I. Bischi and F. Szidarovszky (Editors) "Games and Dynamics in Economics. Essays in Honor of Akio Matsumoto", Springer 2020, 33-67.
• L. Gardini and W. Tikjha, Dynamics in the transition case invertible/noninvertible in a 2D Piecewise Linear Map, Chaos Solitons and Fractals, 137 (2020) 109813, https://doi.org/10.1016/j.chaos.2020.109813
• L. Gardini and W. Tikjha, Milnor and topological attractors in a family of two-dimensional Lotka-Volterra maps, International Journal of Bifurcation and Chaos Vol. 30, No. 14 (2020) 2030040 (29 pages) DOI: 10.1142/S0218127420300402
• Mikhail Anufriev; Laura Gardini; Davide Radi, Chaos, Border Collisions and Stylized Empirical Facts in an Asset Pricing Model with Heterogeneous Agents" Nonlinear Dynamics, 2020, 25 pages, 102:993–1017 https://doi.org/10.1007/s11071-020-05689-1
• Giorgio Calcagnini, Laura Gardini, Germana Giombini, Edgar Sanchez Carrera, Does too much liquidity generate instability? Journal of Economic Interaction and Coordination (JEIC) Received: 5 March 2020 / Accepted: 8 August 2020, 18 pages, https://doi.org/10.1007/s11403-020-00296-0
• Laura Gardini, Celso Grebogi, Stefano Lenci Preface to the Special Issue “Chaos theory and applications: a retrospective on lessons learned and missed or new opportunities” Nonlinear Dynamics (2020) 102:643–644 https://doi.org/10.1007/s11071-020-05903-0(0123456789().,-volV() 0123458697().,-volV)
• Ingrid Kubin and Laura Gardini, On the significance of borders: the emergence of endogenous dynamics, Journal of Economic Interaction and Coordination, 2020 https://doi.org/10.1007/s11403-020-00302-5
• Laura Gardini, Iryna Sushko and Fabio Tramontana, Dynamics of a two-dimensional map on nested circles and rings, Chaos Solitons and Fractals, 143 (2021) 110553 https://doi.org/10.1016/j.chaos.2020.110553
• Laura Gardini , Wirot Tikjha, Bifurcations in a one-parameter family of Lotka-Volterra 2D transformations, Commun Nonlinear Sci Numer Simulat 100 (2021) 105848 (pages 1-17) https://doi.org/10.1016/j.cnsns.2021.105848
• Laura Gardini, Noemi Schmitt, Iryna Sushko, Fabio Tramontana & Frank Westerhoff, Necessary and sufficient conditions for the roots of a cubic polynomial and bifurcations of codimension-1, -2, -3 for 3D maps, Journal of Difference Equations and Applications, 2021 (22 pages) DOI: 10.1080/10236198.2021.1920937
• Mauro Gallegati, Laura Gardini, Iryna Sushko, Dynamics of a business cycle model with two types of governmental expenditures: the role of border collision bifurcations, Decisions in Economics and Finance, 2021 https://doi.org/10.1007/s10203-021-00333-y (27 pages)
• Fabio Tramontana and Laura Gardini, Revisiting Samuelson’s models, linear and nonlinear, stability conditions and oscillating dynamics Journal of Economic Structures (in press)