Search

We analyze the dynamics of a generalized discrete time population model of a two-stage species with recruitment and capture. This generalization, which is inspired by other approaches and real data that one can find in literature, consists in considering no restriction for the value of the two key parameters appearing in the model, that is, the natural death rate and the mortality rate due to fishing activity. In the more general case the feasibility of the system has been preserved by posing opportune formulas for the piecewise map defining the model. The resulting two-dimensional nonlinear map is not smooth, though continuous, as its definition changes as any border is crossed in the phase plane. Hence, techniques from the mathematical theory of piecewise smooth dynamical systems must be applied to show that, due to the existence of borders, abrupt changes in the dynamic behavior of population sizes and multistability emerge. The main novelty of the present contribution with respect to the previous ones is that, while using real data, richer dynamics are produced, such as fluctuations and multistability. Such new evidences are of great interest in biology since new strategies to preserve the survival of the species can be suggested.

This paper tackles the issue of local and global analyses of a duopoly game with price competition and market share delegation. The dynamics of the economy is characterised by a differentiable two-dimensional discrete time system. The paper stresses the importance of complementarity between products as a source of synchronisation in the long term, in contrast to the case of their substitutability. This means that when products are complements, players may coordinate their behaviour even if initial conditions are different. In addition, there exist multiple attractors so that even starting with similar conditions may end up generating very different dynamic patterns.

We study the dynamics shown by the discrete time neoclassical one-sector growth model with differential savings while assuming a nonconcave production function. We prove that complex features exhibited are related both to the structure of the coexixting attractors and to their basins. We also show that complexity emerges if the elasticity of substitution between production factors is low enough and shareholders save more than workers, confirming the results obtained while considering concave production functions.

We consider an asset-pricing model with wealth dynamics in a market populated by heterogeneous agents. By assuming that all agents belonging to the same group agree to share their wealth whenever an agent joins the group (or leaves it), we develop an adaptive model which characterizes the evolution of wealth distribution when agents switch between different trading strategies. Two groups with heterogeneous beliefs are considered: fundamentalists and chartists. The model results in a nonlinear three-dimensional dynamical system, which we have studied in order to investigate complicated dynamics and to explain wealth distribution among agents in the long run.

We consider the dynamics of a stochastic cobweb model with linear demand and a backward-bending supply curve. In our model, forward-looking expectations and backward-looking ones are assumed, in fact we assume that the representative agent chooses the backward predictor with probability 𝑞_,__0_𝑞_1, and the forward predictor with probability (1−𝑞), so that the expected price at time 𝑡 is a random variable and consequently the dynamics describing the price evolution in time is governed by a stochastic dynamical system. The dynamical system becomes a Markov process when the memory rate vanishes. In particular, we study the Markov chain in the cases of discrete and continuous time. Using a mixture of analytical tools and numerical methods, we show that, when prices take discrete values, the corresponding Markov chain is asymptotically stable. In the case with continuous prices and nonnecessarily zero memory rate, numerical evidence of bounded price oscillations is shown. The role of the memory rate is studied through numerical experiments, this study confirms the stabilizing effects of the presence of resistant memory.

This work provides a framework to analyze the role of financial development as a source of endogenous instability in emerging economies subject to moral hazard problems. We propose and study a dynamic model describing a small open economy with a tradeable good produced by internationally mobile capital and a country specific input, using Leontief technology. We demonstrate that emerging markets could be endogenously unstable since large capital inflows increase risk and exacerbate asymmetric information problems, according to empirical evidences. Using bifurcation and stability analysis, we describe the properties of the system attractors, we assess the plausibility for complex dynamics and, we find out that border collision bifurcations can emerge due to the fact that the state space is piecewise smooth. As a consequence, when a fixed or periodic point loses its stability, the final dynamics may become suddenly chaotic. This fact may explain how financial crises occurred in emerging economies.