A simple conceptual model of abrupt glacial climate events

Here we use a very simple conceptual model in an attempt to reduce essential parts of the complex nonlinearity of abrupt glacial climate changes (the so-called Dansgaard-Oeschger events) to a few simple principles, namely (i) the existence of two different climate states, (ii) a threshold process and (iii) an overshooting in the stability of the system at the start and the end of the events, which is followed by a millennial-scale relaxation. By comparison with a so-called Earth system model of intermediate complexity (CLIMBER-2), in which the events represent oscillations between two climate states corresponding to two fundamentally different modes of deep-water formation in the North Atlantic, we demonstrate that the conceptual model captures fundamental aspects of the nonlinearity of the events in that model. We use the conceptual model in order to reproduce and reanalyse nonlinear resonance mechanisms that were already suggested in order to explain the characteristic time scale of Dansgaard-Oeschger events. In doing so we identify a new form of stochastic resonance (i.e. an overshooting stochastic resonance) and provide the first explicitly reported manifestation of ghost resonance in a geosystem, i.e. of a mechanism which could be relevant for other systems with thresholds and with multiple states of operation. Our work enables us to explicitly simulate realistic probability measures of Dansgaard-Oeschger events (e.g. waiting time distributions, which are a prerequisite for statistical analyses on the regularity of the events by means of Monte-Carlo simulations). We thus think that our study is an important advance in order to develop more adequate methods to test the statistical significance and the origin of the proposed glacial 1470-year climate cycle

Intelligent systems in the context of surrounding environment

We investigate the behavioral patterns of a population of agents, each controlled by a simple biologically motivated neural network model, when they are set in competition against each other in the Minority Model of Challet and Zhang. We explore the effects of changing agent characteristics, demonstrating that crowding behavior takes place among agents of similar memory, and show how this allows unique `rogue' agents with higher memory values to take advantage of a majority population. We also show that agents' analytic capability is largely determined by the size of the intermediary layer of neurons. In the context of these results, we discuss the general nature of natural and artificial intelligence systems, and suggest intelligence only exists in the context of the surrounding environment (embodiment). Source code for the programs used can be found at http://neuro.webdrake.net/

Physics of Psychophysics: Stevens and Weber-Fechner laws are transfer functions of excitable media

Sensory arrays made of coupled excitable elements can improve both their input sensitivity and dynamic range due to collective non-linear wave properties. This mechanism is studied in a neural network of electrically coupled (e.g. via gap junctions) elements subject to a Poisson signal process. The network response interpolates between a Weber-Fechner logarithmic law and a Stevens power law depending on the relative refractory period of the cell. Therefore, these non-linear transformations of the input level could be performed in the sensory periphery simply due to a basic property: the transfer function of excitable media.Comment: 4 pages, 5 figure

Effect of Chaotic Noise on Multistable Systems

In a recent letter [Phys.Rev.Lett. {\bf 30}, 3269 (1995), chao-dyn/9510011], we reported that a macroscopic chaotic determinism emerges in a multistable system: the unidirectional motion of a dissipative particle subject to an apparently symmetric chaotic noise occurs even if the particle is in a spatially symmetric potential. In this paper, we study the global dynamics of a dissipative particle by investigating the barrier crossing probability of the particle between two basins of the multistable potential. We derive analytically an expression of the barrier crossing probability of the particle subject to a chaotic noise generated by a general piecewise linear map. We also show that the obtained analytical barrier crossing probability is applicable to a chaotic noise generated not only by a piecewise linear map with a uniform invariant density but also by a non-piecewise linear map with non-uniform invariant density. We claim, from the viewpoint of the noise induced motion in a multistable system, that chaotic noise is a first realization of the effect of {\em dynamical asymmetry} of general noise which induces the symmetry breaking dynamics.Comment: 14 pages, 9 figures, to appear in Phys.Rev.

Mirror symmetry breaking through an internal degree of freedom leading to directional motion

We analyze here the minimal conditions for directional motion (net flow in phase space) of a molecular motor placed on a mirror-symmetric environment and driven by a center-symmetric and time-periodic force field. The complete characterization of the deterministic limit of the dissipative dynamics of several realizations of this minimal model, reveals a complex structure in the phase diagram in parameter space, with intertwined regions of pinning (closed orbits) and directional motion. This demonstrates that the mirror-symmetry breaking which is needed for directional motion to occur, can operate through an internal degree of freedom coupled to the translational one.Comment: Accepted for publication in Phys. Rev.

Multiple current reversals in forced inhomogeneous ratchets

Transport properties of overdamped Brownian paricles in a rocked thermal ratchet with space dependent friction coefficient is studied. By tuning the parameters, the direction of current exhibit multiple reversals, both as a function of the thermal noise strength as well as the amplitude of rocking force. Current reversals also occur under deterministic conditions and exhibits intriguing structure. All these features arise due to mutual interplay between potential asymmetry,noise, driving frequency and inhomogeneous friction.Comment: 6 figure

Dynamical mean-field theory of spiking neuron ensembles: response to a single spike with independent noises

Dynamics of an ensemble of $N$-unit FitzHugh-Nagumo (FN) neurons subject to white noises has been studied by using a semi-analytical dynamical mean-field (DMF) theory in which the original $2 N$-dimensional {\it stochastic} differential equations are replaced by 8-dimensional {\it deterministic} differential equations expressed in terms of moments of local and global variables. Our DMF theory, which assumes weak noises and the Gaussian distribution of state variables, goes beyond weak couplings among constituent neurons. By using the expression for the firing probability due to an applied single spike, we have discussed effects of noises, synaptic couplings and the size of the ensemble on the spike timing precision, which is shown to be improved by increasing the size of the neuron ensemble, even when there are no couplings among neurons. When the coupling is introduced, neurons in ensembles respond to an input spike with a partial synchronization. DMF theory is extended to a large cluster which can be divided into multiple sub-clusters according to their functions. A model calculation has shown that when the noise intensity is moderate, the spike propagation with a fairly precise timing is possible among noisy sub-clusters with feed-forward couplings, as in the synfire chain. Results calculated by our DMF theory are nicely compared to those obtained by direct simulations. A comparison of DMF theory with the conventional moment method is also discussed.Comment: 29 pages, 2 figures; augmented the text and added Appendice

25 Years of Self-organized Criticality: Concepts and Controversies

Introduced by the late Per Bak and his colleagues, self-organized criticality (SOC) has been one of the most stimulating concepts to come out of statistical mechanics and condensed matter theory in the last few decades, and has played a significant role in the development of complexity science. SOC, and more generally fractals and power laws, have attracted much comment, ranging from the very positive to the polemical. The other papers (Aschwanden et al. in Space Sci. Rev., 2014, this issue; McAteer et al. in Space Sci. Rev., 2015, this issue; Sharma et al. in Space Sci. Rev. 2015, in preparation) in this special issue showcase the considerable body of observations in solar, magnetospheric and fusion plasma inspired by the SOC idea, and expose the fertile role the new paradigm has played in approaches to modeling and understanding multiscale plasma instabilities. This very broad impact, and the necessary process of adapting a scientific hypothesis to the conditions of a given physical system, has meant that SOC as studied in these fields has sometimes differed significantly from the definition originally given by its creators. In Bak’s own field of theoretical physics there are significant observational and theoretical open questions, even 25 years on (Pruessner 2012). One aim of the present review is to address the dichotomy between the great reception SOC has received in some areas, and its shortcomings, as they became manifest in the controversies it triggered. Our article tries to clear up what we think are misunderstandings of SOC in fields more remote from its origins in statistical mechanics, condensed matter and dynamical systems by revisiting Bak, Tang and Wiesenfeld’s original papers

The Importance of Representing Cognitive Processes in Multi-Agent Models

We distinguish between two main types of model: predictive and explanatory. It is argued (in the absence of models that predict on unseen data) that in order for a model to increase our understanding of the target system the model must credibly represent the structure of that system, including the relevant aspects of agent cognition. Merely "plugging in" an existing algorithm for the agent cognition will not help in such understanding. In order to demonstrate that the cognitive model matters, we compare two multi-agent stock market models that differ only in the type of algorithm used by the agents to learn. We also present a positive example where a neural net is used to model an aspect of agent behaviour in a more descriptive manner