Papers by Massimiliano Ferrara
Mathematics
This work generalizes Matsumoto et al.’s dynamic model of population and renewable resources by s... more This work generalizes Matsumoto et al.’s dynamic model of population and renewable resources by substituting a distributed delay for the time delay. It is proved that the equilibrium point may lose or gain local stability, allowing for the observation of alternating stability/instability areas if some conditions hold.
WSEAS Transactions on Mathematics archive, Mar 1, 2009
In this paper we extend the study done by Ferrara and Guerrini [12], where two different research... more In this paper we extend the study done by Ferrara and Guerrini [12], where two different research lines within the Ramsey model were joined together: the one studying the role of a logistic population growth rate (Accinelli and Brida [2]), and the one analyzing the effects of a Benthamite formulation for the utility function. The results obtained in [12] for the special case of a constant intertemporal elasticity of substitution (CIES) utility function and a Cobb-Douglas production function are provided to be still true for a general utility function and a neoclassical production function. We have that the model is described by a three dimensional dynamical system, whose unique non-trivial steady state equilibrium is a saddle point with a two dimensional stable manifold. Consequently, the speed of convergence is determined by two stable roots, rather than only one as in the basic Ramsey model. In addition, in the special case of a CIES utility function and a Cobb-Douglas technology, an explicit solution for the model can be derived, when capital's share is equal to the reciprocal of the intertemporal elasticity of substitution.
ArcHistoR Architettura Storia Restauro - Architecture History Restoration, 2020
Today the research into the basic principles for the modeling of economic growth is a new and top... more Today the research into the basic principles for the modeling of economic growth is a new and topical challenge which has been the object of much investigation. Ever since 1862 Spencer has advocated that the economic growth of societies depends on their capability to exploit the increasing amounts of energy. Accordingly, the quantity of energy that a society consumes becomes an economic tool to measure its progress and thus the capital accumulation represents an important strategy for the growth process. In particular, the Solow model, which involves the aggregate production function, has made an important contribution to the economic growth theory especially because it is able to explain the differences between countries in GDP per worker. However, as discussed in Dalgaard and Strulik, the derivation of the law of movement of capital without recurring to the existence of an aggregate production function could be more appropriate. The main aim of this study is to shed light on what ...
Symmetry, 2021
The paper analyzes a two-stage oligopoly game of semi-collusion in production described by a syst... more The paper analyzes a two-stage oligopoly game of semi-collusion in production described by a system with a symmetric structure. We examine the local stability of a Nash equilibrium and the presence of bifurcations. We discover that the model is capable of exhibiting extremely complicated dynamic behaviors.
WSEAS Transactions on Mathematics archive, 2009
This paper generalizes the model introduced by Ferrara and Guerrini [13], where two different res... more This paper generalizes the model introduced by Ferrara and Guerrini [13], where two different research lines have been joined together: the one studying the effects of incorporating technological p...
Symmetry, 2020
The aim of this study is to analyse a discrete-time two-stage game with R&D competition by consid... more The aim of this study is to analyse a discrete-time two-stage game with R&D competition by considering a continuous-time set-up with fixed delays. The model is represented in the form of delay differential equations. The stability of all the equilibrium points is studied. It is found that the model exhibits very complex dynamical behaviours, and its Nash equilibrium is destabilised via Hopf bifurcations.
We extend the Ramsey growth model with logistic population change introduced by J. G. Brida and E... more We extend the Ramsey growth model with logistic population change introduced by J. G. Brida and E. Accinelli [“The Ramsey model with logistic population growth”, Econ. Bull. 3, 1–8 (2007)] by incorporating technological progress in a way similar to P. Duczynski [“Technological diffusion in the Ramsey model”, Int. J. Bus. Econ. 1, No. 3, 243–250 (2006)]. Within this framework, we show that the model is described by a four-dimensional dynamical system with a unique steady-state equilibrium. The transitional dynamics are represented by a three-dimensional stable saddle-path. Thus enriching the transitional adjustment paths relative to that of the standard Ramsey growth model.
Nonlinear Analysis: Modelling and Control, 2014
In this paper, we introduce a time-to-build technology in a Solow model with pollution. We show t... more In this paper, we introduce a time-to-build technology in a Solow model with pollution. We show that Hopf bifurcations occur as the delay passes through critical values. The direction and the stability criteria of the bifurcating periodic solutions are obtained by the normal form theory and the center manifold theorem. Numerical experiments confirm the analytical results with regard to the emergence of nonlinear dynamics.
The increasing interest of EU towards specific structures devoted to stimulate innovation as tech... more The increasing interest of EU towards specific structures devoted to stimulate innovation as technopoles (TP) and science parks (SP) obliges to investigate their role in the overall economic context. The paper examines how performances and characteristics of technopoles and science park affect various aspects of Italian regional economies at NUTS 2 level. Our main aim is to assess the importance of TP and SP in stimulating growth through innovation, as well as entrepreneurship in the area they are established. First, we test the strength of the relationship between poles activities and the performance of firms located in the same region. Second, we investigate whether the presence and number of poles have an impact on both incentives to entrepreneurship and survival rates within their respective region. Finally, we shift our focus to each specific structure in order to test how their characteristics affect market performance of associated firms. Each of the three parts include also an aggregation of results by macro-area. It is important to note how empirical research is mostly descriptive, notwithstanding we are able to deliver a few useful insights that might be relevant to public decision makers.
In article we consider problems modeled by the non-local fractional Laplacian equation (−∆) s u =... more In article we consider problems modeled by the non-local fractional Laplacian equation (−∆) s u = λf (x, u) + µg(x, u) in Ω u = 0 in R n \ Ω, where s ∈ (0, 1) is fixed, (−∆) s is the fractional Laplace operator, λ, µ are real parameters, Ω is an open bounded subset of R n (n > 2s) with Lipschitz boundary ∂Ω and f, g : Ω × R → R are two suitable Carathéodory functions. By using variational methods in an appropriate abstract framework developed by Servadei and Valdinoci [17] we prove the existence of at least three weak solutions for certain values of the parameters.
Известия Российской академии наук. Серия математическая, 2014
Асимптотический предел интегро-дифференциального уравнения, моделирующего сложные системы Проведе... more Асимптотический предел интегро-дифференциального уравнения, моделирующего сложные системы Проведен асимптотический анализ математической модели, которая была недавно предложена для моделирования сложных систем, находящихся под действием внешнего силового поля, в прикладных науках. Эта модель состоит из интегро-дифференциального кинетического уравнения, соединенного с гауссовым изокинетическим термостатом. Асимптотический анализ выполняется в пределе больших значений времени и слабого поля. Показано, что в этом пределе возникает диффузионное поведение в макроскопическом масштабе. Библиография: 50 наименований. Ключевые слова: интегро-дифференциальное уравнение, предел слабого поля, процесс со скачками скорости, активные частицы, кинетическая теория.
ABSTRACT In this paper one generalizes various types of constrained extremism, keeping the Lagran... more ABSTRACT In this paper one generalizes various types of constrained extremism, keeping the Lagrange or Kuhn-Tucker multipliers rule. The context which supports this development is the nonholonomic optimization theory which requires a holonomic or nonholonomic objective function subject to nonholonomic or holonomic constraints. We refined such a problem using two new ideas: the replacement of the point or velocity constraints by a curve selector, and the geometrical interpretation of the Lagrange and Kuhn-Tucker parameters. The classical optimization theory is recovered as a particular case of extremism constrained by a curve selector.
Applied Mathematical Sciences, 2013
This paper reviews the relationship between lags and cycles into classical structures of growth m... more This paper reviews the relationship between lags and cycles into classical structures of growth models (see Solow-Swan and Ramsey models). Some remarks and perspectives of research are determined.
Economic Modelling, 2009
This paper studies how the intertemporal allocation determines the transitional dynamics to a giv... more This paper studies how the intertemporal allocation determines the transitional dynamics to a given steady state and the long-term growth of an economy. Our main contribution consists in determining the solutions path for all the variables of the model, under fairly general conditions on σ and β.
Applied Mathematics & Information Sciences, 2013
The economic growth model with endogenous labor shift under a dual economy proposed by Cai [Appli... more The economic growth model with endogenous labor shift under a dual economy proposed by Cai [Applied Mathematics Letters 21, 774-779 (2008)] is generalized in this paper by introducing a time delay in the physical capital. By choosing the delay as a bifurcation parameter, it is proved that the delayed model has unique nonzero equilibrium and a Hopf bifurcation is proven to exist as the delay crosses a critical value. Moreover the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are investigated in this paper by applying the center manifold theorem and the normal form theory.
In this paper, we study the equilibrium dynamics of an endogenous growth model with endogenous fe... more In this paper, we study the equilibrium dynamics of an endogenous growth model with endogenous fertility choice. In this setting, we show that there is a unique equilibrium which is globally determinated. The validity of the neo-Malthusian relation between fertility and growth is then examined.
The innovation process is a fundamental source of economic growth and recent research in urban ec... more The innovation process is a fundamental source of economic growth and recent research in urban economics and economic geography suggests that geographical proximity between innovators may be important to technological innovation. Many authors also claim that the rise of a knowledge-based economy and changes in the organization of the innovation process have actually increased the value of such proximity to innovation. But yet there is little empirical research on how knowledge flows between developed countries to developing ones and vice versa. A high level of consensus exists regarding the importance of scientific progress and technological innovation for the growth and competitiveness of firms and for the improvement of national economic performance. Most of the literature focus on international technology diffusion between developed countries, The literature emphasize principally on three channel for the international knowledge diffusion: the international trade that assures free access to knowledge embodied in imported goods (Coe and Helpman 1995) and knowledge in global export markets through "learning by exporting" (Bernard and Jensen 1999) and the contact with advanced foreign firms; the labour mobility that is source of knowledge exchange because workers are endowed with specific know-how (Rhee 1990, Pesola, 2007); and finally foreign direct investment (FDI) (Blomstrom and Kokko 1998, Aitken and Harrison 1999, Crespo and Fontoura 2007) that represents an important source of technological spillovers although the empirical evidence remains mixed with regards to the distributions of benefits between the multinational and domestic companies. In order to test the existence of a further channel in international knowledge diffusion, some recent empirical work analysed in a knowledge production framework (KPF) (Murseth and Verspagen 2002, Bottazzi and Peri 2003, Peri 2005). At sectoral level, Malerba et al. (2007) found that extremely relevant sectoral knowledge flows cross national borders. Only few make a relationship between developing countries and developed ones. Coe et al. (1997) examined north-south R&D spillover. They found that total factor productivity in developing countries is significantly boosted by the R&D stock of industrial countries, which they computed as the import-share-weighted sum of the R&D expenditures of a developing country's trading partners in the north. They interpreted this as evidence of north-south R&D spillover. Hu and Jaffe (2003) examined patterns of knowledge diffusion from U.S. and Japan to Korea and Taiwan using patent citations. They found that Korean patents are more likely to cite Japanese patents than U.S. ones, maybe due to their proximity. They also found that both Korea and Taiwan are surprisingly reliant on relatively recent technology. A comparison of patterns in knowledge diffusion from the US and South East Asia (Korea and Taiwan) and Latina America (Brazil and Mexico) from 1976 till 2002 has been presented in the IV Globelics Conference at Mexico City. Aboites and Beltran (2008) conclusion were that the patterns of knowledge diffusion from US to Latin American and South East Asian countries are quite different. They found that the South East had a higher number of patents granted in USPTO than their Latin American counterparts and the technologies registered in Korea and Taiwan were of high technology (Information and Communications, Electric and Electronics, etc.) meanwhile in Latin America (Brazil and Mexico) the technologies registered were of traditional tech fields (mechanical, chemical, etc.). In their studies, they found also that the citations received (forward) by Korea and Taiwan outnumber the citations received by Mexico and Brazil. That means that the value of knowledge in Asian countries. Montobbio and Sterzi (2008) analysed nature, sources and determinants of international patenting activity in Latin American countries and the extent to which these countries benefit from R&D performed in some developed countries, using a patent citation analysis. They found that that the stock of ideas produced in the US has a strong impact on the international patenting activity of these countries. The purpose of this paper is to investigate the pattern of knowledge flows and technological trajectories, as indicated by patent citations, between North Saharan (NS) countries and South European (SE) countries and explore the nature of these flows during the 1984-2003 period. The results describes the patterns of knowledge diffusion for the NS area counties and SE area countries during the 1983-2004 period are quite different. We found that, obviously, the SE area countries had a higher number of patents granted in EPO than the NS area countries. Furthermore, the technologies registered in SE area countries were evenly distributed across sector meanwhile in NS countries the technologies registered were of traditional tech fields and tend to exclude the Mechanical Elements/Machine Tools/Transport and the Consumer goods sectors. That means that the value of knowledge in SE area countries is more important that the value of NS area countries. The other strong finding, to be further investigate, is the extremely high speed of knowledge diffusion seen both in forward and backward citations from/to the NS area countries for the sector of industrial process.
ABSTRACT We modify the Ramsey model with von Bertalanffy population growth law by assuming that c... more ABSTRACT We modify the Ramsey model with von Bertalanffy population growth law by assuming that capital is not produced instantaneously but produced and installed after some period. We prove that the introduction of a delay causes the model to have a Hopf bifurcation.
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Papers by Massimiliano Ferrara