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On the error in approximating stability spectra for discrete dynamical systems

Menning, Melissa; Vleck, Erik S. Van - In: Mathematics and Computers in Simulation (MATCOM) 81 (2011) 5, pp. 1006-1016

In this work, we develop a perturbation theory for the approximation of stability spectra (Lyapunov exponents and Sacker-Sell spectrum) for discrete time dynamical systems. The approach is based upon QR based methods that transform linear time varying discrete time systems to an upper triangular...

Persistent link: https://www.econbiz.de/10010870523

On stabilizing volatile product returns

Nowak, Thomas; Hofer, Vera - In: European Journal of Operational Research 234 (2014) 3, pp. 701-708

As input flows of secondary raw materials show high volatility and tend to behave in a chaotic way, the identification of the main drivers of the dynamic behavior of returns plays a crucial role. Based on a stylized production-recycling system consisting of a set of nonlinear difference...

Persistent link: https://www.econbiz.de/10010871183

Robust optimal control of material flows in demand-driven supply networks

Laumanns, Marco; Lefeber, Erjen - In: Physica A: Statistical Mechanics and its Applications 363 (2006) 1, pp. 24-31

We develop a model based on stochastic discrete-time controlled dynamical systems in order to derive optimal policies for controlling the material flow in supply networks. Each node in the network is described as a transducer such that the dynamics of the material and information flows within...

Persistent link: https://www.econbiz.de/10010872298

A probabilistic framework for hysteresis

Grinfeld, M.; Piscitelli, L.; Cross, R. - In: Physica A: Statistical Mechanics and its Applications 287 (2000) 3, pp. 577-586

We introduce a probabilistic framework for hysteresis, a ubiquitous phenomenon in economic situations involving sunk costs. The framework is applied to a simple model of a firm's market entry/exit decisions. We study the influence of sunk cost size, width of the hysteretic loop, and of...

Persistent link: https://www.econbiz.de/10010873637

Binary choices in small and large groups: A unified model

Bischi, Gian-Italo; Merlone, Ugo - In: Physica A: Statistical Mechanics and its Applications 389 (2010) 4, pp. 843-853

Two different ways to model the diffusion of alternative choices within a population of individuals in the presence of social externalities are known in the literature. While Galam’s model of rumors spreading considers a majority rule for interactions in several groups, Schelling considers...

Persistent link: https://www.econbiz.de/10010874062

Some global bifurcations related to the appearance of closed invariant curves

Agliari, Anna; Gardini, Laura; Puu, Tönu - In: Mathematics and Computers in Simulation (MATCOM) 68 (2005) 3, pp. 201-219

In this paper, we consider a two-dimensional map (a duopoly game) in which the fixed point is destabilized via a subcritical Neimark–Hopf (N–H) bifurcation. Our aim is to investigate, via numerical examples, some global bifurcations associated with the appearance of repelling closed...

Persistent link: https://www.econbiz.de/10011050483

Factorization properties of birational mappings

Boukraa, S; Maillard, J-M - In: Physica A: Statistical Mechanics and its Applications 220 (1995) 3, pp. 403-470

We analyse birational mappings generated by transformations on q × q matrices which correspond respectively to two kinds of transformations: the matrix inversion and a permutation of the entries of the q × q matrix. Remarkable factorization properties emerge for quite general involutive...

Persistent link: https://www.econbiz.de/10011058919

New integrable cases of a Cremona transformation: a finite-order orbits analysis

Boukraa, S.; Hassani, S.; Maillard, J.-M. - In: Physica A: Statistical Mechanics and its Applications 240 (1997) 3, pp. 586-621

We analyse the properties of a particular birational mapping of two variables (Cremona transformation) depending on two free parameters (ε and α), associated with the action of a discrete group of non-linear (birational) transformations on the entries of a q × q matrix. This mapping...

Persistent link: https://www.econbiz.de/10011060945

Multistability in a dynamic Cournot game with three oligopolists

Nabih Agiza, Hamdy; Italo Bischi, Gian; Kopel, Michael - In: Mathematics and Computers in Simulation (MATCOM) 51 (1999) 1, pp. 63-90

-connected sets, a basin structure which is peculiar of non-invertible maps. The presence of several coexisting attractors (or … multistability) is observed even when complex attractors exist. Two different routes to complexity are presented: one related to the … creation of more and more complex attractors; the other related to the creation of more and more complex structures of the …

Persistent link: https://www.econbiz.de/10010749781

Complex dynamics associated with the appearance/disappearance of invariant closed curves

Foroni, Ilaria; Agliari, Anna - In: Mathematics and Computers in Simulation (MATCOM) 81 (2011) 8, pp. 1640-1655

In this paper we study some global bifurcations arising in a heterogeneous financial model with fundamentalists and imitators. Such bifurcations which cause the appearance and disappearance of closed invariant curves (attracting or repelling) involve the stable and unstable sets of a saddle...

Persistent link: https://www.econbiz.de/10010750162