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Dynamics in piecewise linear and continuous models of complex switching networks

Shahrear, Pabel; Glass, Leon; Wilds, Roy; Edwards, Rod - In: Mathematics and Computers in Simulation (MATCOM) 110 (2015) C, pp. 33-39

Activities of genes are controlled in a combinatorial fashion by the concentrations of chemical called transcription factors. We model this type of network by piecewise linear differential equations formed by embedding a logical switching network in a differential equation. We generate...

Persistent link: https://www.econbiz.de/10011264180

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

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

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

Computational complexity of iterated maps on the interval

Spandl, Christoph - In: Mathematics and Computers in Simulation (MATCOM) 82 (2012) 8, pp. 1459-1477

The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The correctness of the algorithm is shown and the...

Persistent link: https://www.econbiz.de/10010751792