Search results for "AOT"
showing 10 items of 347 documents
Experimental study of electrical FitzHugh-Nagumo neurons with modified excitability
2006
International audience; We present an electronical circuit modelling a FitzHugh-Nagumo neuron with a modified excitability. To characterize this basic cell, the bifurcation curves between stability with excitation threshold, bistability and oscillations are investigated. An electrical circuit is then proposed to realize a unidirectional coupling between two cells, mimicking an inter-neuron synaptic coupling. In such a master-slave configuration, we show experimentally how the coupling strength controls the dynamics of the slave neuron, leading to frequency locking, chaotic behavior and synchronization. These phenomena are then studied by phase map analysis. The architecture of a possible ne…
Coexistence of single-mode and multi-longitudinal mode emission in the ring laser model
2005
A homogeneously broadened unidirectonal ring laser can emit in several longitudinal modes for large enough pump and cavity length because of Rabi splitting induced gain. This is the so called Risken-Nummedal-Graham-Haken (RNGH) instability. We investigate numerically the properties of the multi-mode solution. We show that this solution can coexist with the single-mode one, and its stability domain can extend to pump values smaller than the critical pump of the RNGH instability. Morevoer, we show that the multi-mode solution for large pump values is affected by two different instabilities: a pitchfork bifurcation, which preserves phase-locking, and a Hopf bifurcation, which destroys it.
Subharmonic and homoclinic bifurcations in the driven and damped sine-Gordon system
1999
Abstract Chaotic responses induced by an applied biharmonic driven signal on the sine-Gordon (sG) system influenced by a constant dc-driven and the damping fields are investigated using a collective coordinate approach for the motion of the breather in the system. For this biharmonic signal, one term has a large amplitude at low frequency. Thus, the classical Melnikov method does not apply to such a system; however, we use the modified version of the Melnikov method to homoclinic bifurcations of the perturbed sG system. Additionally resonant breathers are studied using the modified subharmonic Melnikov theory. This dynamic behavior is illustrated by some numerical computations.
FILTERING CHAOS: A TECHNIQUE TO ESTIMATE DYNAMICAL AND OBSERVATIONAL NOISE IN NONLINEAR SYSTEMS
2005
Nonlinear dynamical models are frequently used to approximate and predict observed physical, biological and economic systems. Such models will be subject to errors both in the model dynamics, and the observations of the underlying system. In order to improve models, it is necessary to understand the causes of error growth. A complication with chaotic models is that small errors may be amplified by the model dynamics. This paper proposes a technique for estimating levels of both dynamical and observational noise, based on the model drift. The method is demonstrated for a number of models, for cases with both stochastic and nonstochastic dynamical errors. The effect of smoothing or treating …
Noise-induced behavioral change driven by transient chaos
2022
We study behavioral change in the context of a stochastic, non-linear consumption model with preference adjusting, interdependent agents. Changes in long-run consumption behavior are modelled as noise induced transitions between coexisting attractors. A particular case of multistability is considered: two fixed points, whose immediate basins have smooth boundaries, coexist with a periodic attractor, with a fractal immediate basin boundary. If a trajectory leaves an immediate basin, it enters a set of complexly intertwined basins for which final state uncertainty prevails. The standard approach to predicting transition events rooted in the stochastic sensitivity function technique due to Mil…
A Review of Mathematical and Computational Methods in Cancer Dynamics.
2022
Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires the integration of information dynamics across multidimensional spatiotemporal scales, including genetic, transcriptional, metabolic, proteomic, epigenetic, and multi-cellular networks. However, the time-series analysis of these complex networks remains vastly absent in cancer research. With longitudinal screening and time-series analysis of cellular dynamics, universally observed causal patterns pertaining to dynamical systems, may self-organize in the si…
Ideal Chaotic Pattern Recognition is achievable: The Ideal-M-AdNN - its design and properties
2013
Published version of a chapter in the book: Transactions on Computational Collective Intelligence XI. Also available from the publisher at: http://dx.doi.org/10.1007/978-3-642-41776-4_2 This paper deals with the relatively new field of designing a Chaotic Pattern Recognition (PR) system. The benchmark of such a system is the following: First of all, one must be able to train the system with a set of “training” patterns. Subsequently, as long as there is no testing pattern, the system must be chaotic. However, if the system is, thereafter, presented with an unknown testing pattern, the behavior must ideally be as follows. If the testing pattern is not one of the trained patterns, the system …
Exchange rates expectations and chaotic dynamics: a replication study
2018
Abstract In this paper the author analyzes the behavior of exchange rates expectations for four currencies, by considering a re-calculation and an extension of Resende and Zeidan (Expectations and chaotic dynamics: empirical evidence on exchange rates, Economics Letters, 2008). Considering Lyapunov exponent-based tests results, they are not supportive of chaos in exchange rates expectations, although the so-called 0–1 test strongly supports the chaos hypothesis.
Chaotic dynamics in an unstirred ferroin catalyzed Belousov–Zhabotinsky reaction
2009
Abstract The Belousov–Zhabotinsky (BZ) reaction is the best known example of far from equilibrium self-organizing chemical reaction. Among the many dynamical behaviors that this reaction can exhibit, spatio-temporal chaos attracted particular interest, both for the ferroin and cerium catalyzed systems. In recent years transient chaos was found in the cerium catalyzed BZ reaction, when conducted in batch and unstirred reactors. It was established that the chaotic oscillations, originated by the coupling among chemical kinetics and transport phenomena, appeared and disappeared following a Ruelle–Takens–Newhouse scenario. In this Letter, we show results about the ferroin catalyzed system condu…
On differences and similarities in the analysis of Lorenz, Chen, and Lu systems
2015
Currently it is being actively discussed the question of the equivalence of various Lorenzlike systems and the possibility of universal consideration of their behavior (Algaba et al., 2013a,b, 2014b,c; Chen, 2013; Chen and Yang, 2013; Leonov, 2013a), in view of the possibility of reduction of such systems to the same form with the help of various transformations. In the present paper the differences and similarities in the analysis of the Lorenz, the Chen and the Lu systems are discussed. It is shown that the Chen and the Lu systems stimulate the development of new methods for the analysis of chaotic systems. Open problems are discussed. peerReviewed