Narrow Results

A multi-agent spin model for changes of prices in the stock market is considered, based on the Ising-like cellular automaton with global, randomly varying in time interactions between traders. The presence of "fundamentalists" is taken into account by introducing additional term in the local field acting on each agent, dependent on the ratio between the actual stock price and its fundamental value. Numerical multi-agent as well as mean-field simulations show that for properly chosen parameters, the time series of logarithmic price returns exhibit bursting typical of volatility clustering, due to appearance of attractor bubbling in the model. Distributions of price returns show the power-law tails, and the corresponding cumulative distributions have regions of power scaling, with exponents comparable to those observed in empirical time series of stock price returns.

We introduce the standard Rössler oscillator and extend it from a system defined on ℝ³ to a system defined on . We extend the system in such a way that the simple Rössler type dynamics are preserved, whilst introducing an additional symmetry to the system such that when the oscillators are linearly coupled, there exists an embedding of symmetry forced invariant manifolds. We contrast our results with a previously considered model for a linearly coupled solid-state laser system which possessed a similar embedding of invariant manifolds. We discuss whether the mechanisms for loss of synchronization are system dependent or a more generic property of systems with embedded invariant manifolds.

We show that coupled Kerr and Duffing oscillators with small nonlinearities and strong external pumping can generate chaotic and hyperchaotic beats. The appearance of chaos within beats depends strongly on the type of interactions between the nonlinear oscillators. To indicate chaotic behavior of the system we make use of the Lyapunov exponents. The structure of chaotic beats can be qualitatively different — the envelope function can be smooth if the system is undamped or can give the impression of noise structure in the presence of strong damping and nonlinear interactions between the individual oscillators. The systems considered can be used, in practice, as generators of chaotic beats with chaotically modulated envelopes and frequencies.

To study the mechanism by which high-dimensional chaos emerges in neural systems, the synchronization of chaotic firings in class 1 pulse neural networks composed of excitatory and inhibitory ensembles was analyzed. In the system with two modules (i.e. two pulse neural networks), blowout bifurcation and on–off intermittency were observed when the inter-module connection strengths were reduced from large values. In the system with three modules, rearrangement of synchronized clusters and chaotic itinerancy were observed. Such dynamics may be one of the mechanisms through which high-dimensional chaos is generated in neural systems.

Bursting behaviors, driven by environmental variability, can substantially influence ecosystem services and functions and have the potential to cause abrupt population breakouts in host–parasitoid systems. We explore the impact of environment on the host–parasitoid interaction by investigating separately the effect of grazing-dependent habitat variation on the host density and the effect of environmental fluctuations on the average host population growth rate. We hence focus on the discrete host–parasitoid Beddington–Free–Lawton model and show that a more comprehensive mathematical study of the dynamics behind the onset of on–off intermittency in host–parasitoid systems may be achieved by considering a deterministic, chaotic system that represents the dynamics of the environment. To this aim, some of the key model parameters are allowed to vary in time according to an evolution law that can exhibit chaotic behavior. Fixed points and stability properties of the resulting 3D nonlinear discrete dynamical system are investigated and on–off intermittency is found to emerge strictly above the blowout bifurcation threshold. We show, however, that, in some cases, this phenomenon can also emerge in the sub-threshold. We hence introduce the novel concept of long-term reactivity and show that it can be considered as a necessary condition for the onset of on–off intermittency. Investigations in the time-dependent regimes and kurtosis maps are provided to support the above results. Our study also suggests how important it is to carefully monitor environmental variability caused by random fluctuations in natural factors or by anthropogenic disturbances in order to minimize its effects on throphic interactions and protect the potential function of parasitoids as biological control agents.

The finding of clustered volatility and ARCH effects is ubiquitous in financial data. This paper presents a possible explanation for this phenomenon within a multi-agent framework of speculative activity. In the model, both chartist and fundamentalist strategies are considered with agents switching between both behavioural variants according to observed differences in pay-offs. Price changes are brought about by a market maker reacting to imbalances between demand and supply. Most of the time, a stable and efficient market results. However, its usual tranquil performance is interspersed by sudden transient phases of destabilisation. An outbreak of volatility occurs if the fraction of agents using chartist techniques surpasses a certain threshold value, but such phases are quickly brought to an end by stabilising tendencies. Formally, this pattern can be understood as an example of a new type of dynamic behaviour known as "on-off intermittency" in physics literature. Statistical analysis of simulated time series shows that the main stylised facts (unit roots in levels together with heteroscedasticity and leptokurtosis of returns) can be found in this "artificial" market.

The fluctuations observed in the task of stick balancing at the fingertip exhibit many of the properties predicted to occur in parametric stochastic dynamical systems, namely intermittency, truncated Lévy flights and truncated Lévy distributions. The development of virtual balancing tasks that involve the interplay between a human and computer and that exhibit the same dynamical properties as seen for stick balancing opens the door for experimental investigations into the nature of the neural motor control mechanisms that underlie these phenomena.

The paper examines the appearance of on-off intermittency and riddled basins of attraction in a system of two coupled one-dimensional maps, each displaying type-III intermittency. The bifurcation curves for the transverse destablilization of low periodic orbits embeded in the synchronized chaotic state are obtained. Different types of riddling bifurcation are discussed, and we show how the existence of an absorbing area inside the basin of attraction can account for the distinction between local and global riddling as well as for the distinction between hysteric and non-hysteric blowout. We also discuss the role of the so-called mixed absorbing area that exists immediately after a soft riddling bifurcation. Finally, we study the on-off intermittency that is observed after a non-hysteric blowout bifurcaton.

On markets with receding prices, artificial noise traders may consider alternatives to buy-and-hold. By simulating variations of the Parrondo strategy, using real data from the Swedish stock market, we produce first indications of a buy-low-sell-random Parrondo variation outperforming buy-and-hold. Subject to our assumptions, buy-low-sell-random also outperforms the traditional value and trend investor strategies. We measure the success of the Parrondo variations not only through their performance compared to other kinds of strategies, but also relative to varying levels of perfect information, received through messages within a multi-agent system of artificial traders.