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In this paper, looking at some new contributions to the Kalecki business cycle theory, we re-examine his 1935 model concerning the gestation period between orders and deliveries of capital goods. The model gives rise to a delay differential equation (DDE) with delay dependent coefficients depending on the time delay. The model has only one equilibrium point. Proved that a unique stability switch exists, we study the emergence of the Hopf bifurcation and the direction, stability and period of the bifurcating periodic solutions. We derive an explicit formula for determining the properties of the Hopf bifurcation by using the first Lyapunov coefficient. To confirm our analytic results, we consider two types of non-linear functions, all consistent with Kalecki's hypotheses: two S-shaped functions and one fractional function. Some comments dealing with the economic implications of our analysis are also included. • Kalecki's model of the investment cycle. • Model with time delays and delay dependent coefficients. • Existence of Hopf bifurcations analyzed by choosing time delays as bifurcation parameters. [ABSTRACT FROM AUTHOR]

• The proposed real economy model grounds on a nonlinear multiplier–accelerator setup. • The interplay between monetary and fiscal policy rules is investigated. • The monetary policy is able to lead the economy toward the targeted level of output. • Policies can be the source of endogenous fluctuations resembling business cycle. • The interplay between policies is responsible for the occurrence of multistability. In this paper we consider a nonlinear model for the real economy described by a multiplier–accelerator setup. The model comprises the government sector, which influences the output dynamics by means of the fiscal policy, and the money market, where the money supply depends upon the fluctuations in the economic activity. Through rigorous analytical tools combined with numerical simulations, we investigate the stability conditions of the unique steady state and the emergence of different kinds of endogenous dynamics, which are the results of the action of the fiscal and the monetary policy through their reactivity degrees. Such policies, if properly tuned, can lead the economy toward the desired full employment target but, on the other hand, can also generate endogenous fluctuations in the pace of the economic activity, associated with the occurrence of closed invariant curves and multistability phenomena. [ABSTRACT FROM AUTHOR]

In the process of research and development (R&D) projects on new drugs, firms must face many challenges. The most serious challenges mainly come from economic fluctuations, technical risks, uncertainty of decision-maker's subjective judgment. Troubled by these uncertain factors, how we can accurately evaluate new drug R&D projects is a very urgent and necessary problem for the management of firms. In this paper, we present a new value model on a compound real option to evaluate the new drug R&D project under economic fluctuations, technical risks and subjective uncertainty. The randomness and fuzziness of economic fluctuations are modeled by a standard fractional Brownian motion and a trapezoidal fuzzy stochastic process, respectively. The technical risks are expressed by a Poisson-type jump process, which allows for the catastrophic impact of the technical risk and thus abandonment of the new drug R&D project. The uncertainty of decision-maker's subjective judgment is characterized by a mean value with the possibility–necessity weight, the pessimistic–optimistic index and the fuzzy risk aversion index. By using the real options approach, we achieve analytic solutions for the value models of new drugs R&D projects. A case study and analysis is also employed to emphasize the practical application of this innovative value model. We show that the uncertainties have a significant impact on the new drug R&D option value to some extent. Moreover, from the case of sensitivity analysis, some results are presented to illustrate that the value of new drug R&D project is increasing with respect to the right fuzzy factor and decreasing with respect to the left fuzzy factor, the technical risk of discovery phase, the technical risk of pre-clinical phase and the technical risk of clinical phase. [ABSTRACT FROM AUTHOR]

In this paper we study a simple model based on the cobweb demand-supply framework with costly innovators and free imitators. The evolutionary selection between technologies depends on a performance measure which is related to the degree of memory. The resulting dynamics is described by a two-dimensional map. The map has a fixed point which may lose stability either via supercritical Neimark–Sacker bifurcation or flip bifurcation and several multistability situations exist. We describe some sequences of global bifurcations involving attracting and repelling closed invariant curves. These bifurcations, characterized by the creation of homoclinic connections or homoclinic tangles, are described through several numerical simulations. Particular bifurcation phenomena are also observed when the parameters are selected inside a periodicity region. [ABSTRACT FROM AUTHOR]

Dynamics of Goodwin’s accelerator business cycle model is reconsidered. The model is characterized by a nonlinear accelerator and an investment time delay. The role of the nonlinearity for the birth of persistent oscillations is fully discussed in the existing literature. On the other hand, not much of the role of the delay has yet been revealed. The purpose of this paper is to show that the delay really matters. In the original framework of Goodwin [6] , it is first demonstrated that there is a threshold value of the delay: limit cycles arise for smaller values than the threshold and so do sawtooth oscillations for larger values. In the extended framework in which a consumption or saving delay, in addition to the investment delay, is introduced, three main results are demonstrated under assumption of the identical length of investment and consumption delays. The dynamics with consumption delay is basically the same as that of the single delay model. Second, in the case of saving delay, the steady state can coexist with the stable and unstable limit cycles in the stable case. Third, in the unstable case, there is an interval of delay in which the limit cycle or the sawtooth oscillation emerges depending on the choice of the constant initial function. [ABSTRACT FROM AUTHOR]

To analyze the effect of animal spirits on economic dynamics, we construct a simple Keynesian business-cycle model with animal spirits incorporated into it. Similar to the well-known Kaldor model, we assume that each firm possesses the investment function depending on demand, in which the animal spirits are connected with the degree of the propensity to invest. However, we would like to emphasize that, unlike the Kaldor model, even if the level of demand for each firm is the same, the degree of propensity to invest (i.e., the strength of animal spirits) depends on the change in demand. Thus, we assume that animal spirits in demand-upswing phases are stronger than those in demand-downswing phases. In each phase, the degree of dependence on demand is firm specific. Therefore, we adopt a statistical approach to connect such heterogeneous micro-investment behaviors with a macro-investment function. Through this approach, some kind of nonlinearity is naturally introduced into the macro-investment function. We demonstrate that the nonlinear macro-investment function yields persistent business cycles. We also demonstrate the occurrence of a generalized Hopf bifurcation. • We change of the title of the paper, that is, entitled a new title according to reviewer's comment. • We have made the text as easy to understand as possible including corrections of not only theoretical points but also grammatical and stylistic ones. • We also tried to reduce the number of pages. [ABSTRACT FROM AUTHOR]

This paper investigates the interconnections between real economy and the financial market in a discrete dynamical framework. We focus on the effect of the dividend policy decided by managers and the expectations of investors about future payments. We found that an excessively high dividend payout ratio erodes the economy, while in the opposite case instability and fluctuations arise. By means of analytical results and numerical simulations we show that the positive return of government bonds leads to instability, while investors' expectations modify the path of the asset price. • We investigate the co-evolution of physical capital and a financial asset. • An excessively high dividend payout ratio may erode the economy. • A low dividend payout might cause economic fluctuations. • Positive returns for government bonds lead to instability. • Unfulfilled expectations over dividends affect the path of the asset price. [ABSTRACT FROM AUTHOR]

The Hicksian multiplier–accelerator model with a floor and/or a ceiling stands as one of the most successful representations of the economy capable of generating endogenous business cycles. In the present paper, we take some of the main insights of this literature as starting points to develop a continuous-time growth-cycle model for a small open economy. Our main innovation lies in assuming that capital accumulation is constrained only from above by the growth rate compatible with equilibrium in the balance-of-payments, i.e. the dynamic Harrod trade multiplier. It is shown that the obtained piecewise second order differential equation is a so-called two-stroke oscillator. Conditions under which the model produces periodic or aperiodic trajectories are studied analytically and through numerical simulations. An initial assessment of the statistical properties of the time-series indicates that they exhibit high kurtosis and negative skewness. • We develop an open economy growth cycle model based on the multiplier–accelerator. • Capital accumulation is constrained only from above by the dynamic trade-multiplier. • The resulting piecewise second order differential equation is a two-stroke oscillator. • Introducing a forcing term into autonomous demand leads to more complex dynamics. • Similar results follow from allowing exogenous cycles in international credit markets. • Time-series generated by the model exhibit high kurtosis and negative skewness. [ABSTRACT FROM AUTHOR]

This paper, following Kaldor’s approach, is written with the intention of interpreting fluctuations of economic systems (i.e trade cycles). In particular, a new discretized Kaldor model is proposed, which is also useful to explain what appears to be random and unpredictable, such as economic shocks. Moreover, by using numerical analysis, the chaoticity of the model is demonstrated. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the dynamics of a delayed business cycle model with general investment function. The model describes the interaction of the gross product and capital stock. Furthermore, the delay represents the time between the decision of investment and implementation. Firstly, we show that the model is well posed by proving the global existence and boundedness of solutions. Secondly, we determine the economic equilibrium of the model. By analyzing the characteristic equation, we investigate the stability of the economic equilibrium and the local existence of Hopf bifurcation. Also, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theory. Moreover, the global existence of bifurcating periodic solutions is established by using the global Hopf bifurcation theory. Finally, our theoretical results are illustrated with some numerical simulations. [ABSTRACT FROM AUTHOR]

• The conditions and the critical coefficients of bifurcations of a Kaldor model of business cycle with discrete-time are computed. • All codimension one and codimension two bifurcations of Kaldor model of business cycle with discrete- time are surveyed thoroughly. • The non-degeneracy conditions and predict the bifurcation scenarios are analyzed analytically. • The bifurcations of the higher iterations up to the sixteen iteration are revealed. • There is an excellent agreement between the analytical predictions and the numerical observations. This paper studies the dynamical behavior of a Kaldor model of business cycle with discrete-time analytically and numerically. The conditions and the critical coefficients for the flip (period-doubling), Neimark-Sacker, and strong resonances are computed analytically. By using the critical coefficients, the bifurcation scenarios are determined for each of the deleted bifurcation points. Bifurcation curves of fixed points and cycles with periods up to sixteen by changing one and two parameters along with all codim-1 and codim-2 bifurcations on the corresponding curves are computed using the numerical continuation method. Numerical analysis confirms our analytical results and reveals more complex dynamical behaviors. [ABSTRACT FROM AUTHOR]

• We compute topological entropy of the symmetric cubic business model. • We also consider a non-symmetric cubic map in order to find the parametric region in which chaos exists. • We analyze dynamics of the non-symmetric cubic map using different tools as Lyapunov exponent and topological entropy. Puu [38] introduced a symmetric business cycle model with a cubic investment function depending on a parameter, nevertheless the fact that symmetry is not a needed condition for the investment function was highlighted in [40]. In this paper, the model for business cycles proposed by Puu is revisited using a topological entropy approach, in particular, we prove the existence of topological chaos for a wide range of parameter values. Moreover, a non-symmetric cubic investment map generalizing the model introduced by Puu is considered, giving answer to the posed question. [ABSTRACT FROM AUTHOR]

The use of nonlinear dynamical systems in economics is essential to explain, replicate and govern important phenomena and empirical facts, such as endogenous business cycles, poverty traps, indeterminacy, boom-bust dynamics in time series of asset prices and the excess volatility in financial asset returns. This special issue of Chaos, Solitons & Fractals contains a selection of refereed papers presented at the tenth MDEF Workshop held at the Department of Economics, Society, Politics of the University of Urbino, on the 6-8th September 2018. Able to replicate many of the stylized facts observed in the asset price dynamics, these models are employed to test the ability of regulations and policy interventions in stabilizing the financial markets. [Extracted from the article]

• Existence and stability of limit cycles by way of Hopf bifurcations are rigorously examined in a two-sector Keynesian model of business cycles. • Conditions for emergence and stability of limit cycles are presented. • Numerical simulations confirming the validity of achieved results are demonstrated. The paper investigates a two-sector Keynesian model of business cycles, describing the fluctuations of consumption and investment goods. It makes an analysis of issues concerning the existence of limit cycles around its equilibrium. There is derived the bifurcation equation of the model, giving conditions for the existence of limit cycles and their stability. The achieved results are illustrated on an example with numerical simulations. [ABSTRACT FROM AUTHOR]