Search results for "Complex dynamics"
showing 8 items of 28 documents
Manipulating dissipative soliton ensembles in passively mode-locked fiber lasers
2014
International audience; We review our recent experimental and theoretical results addressing the dynamics of large numbers of solitons interacting in presence of a background in passively mode-locked erbium-doped fiber lasers. We first characterize experimentally the soliton rain complex dynamics, and then we focus on ordered soliton patterns. We report that, for suitable experimental parameters, a continuous wave can impose harmonic mode locking. Two levels of modeling for a mode-locked laser subjected to the external injection of a continuous wave are developed to support the latter observation. The first one is based on a scalar master equation, while the second one takes into account th…
Reduced dynamical equations for solid-state lasers and VCSELs
2007
It is the aim of this presentation to show that a reduction in the number of coupled equations is feasible for spatio-temporal laser models with generic values of the pump and other parameters. Reduced equations have been derived via the application of two separate, yet equivalent, methods: one based on the CM and the other on operational calculus. The long term dynamics of the reduced models for solid-state lasers and VCSELs have been compared with that of the full systems by using both mathematical methods. Extensive numerical simulations for the complex dynamics of these and other laser models become suddenly feasible within reasonable computational time.
A Mushroom Bodies inspired spiking network for classification and sequence learning
2015
Sequence learning is a complex capability shown by living beings, able to extract information from the environment. Looking into the insect world, there are several examples where the presentation time of specific stimuli is considered to select the proper behavioural response. On the basis of previously developed neural models for sequence learning, inspired by the Drosophila melanogaster, a new formalization of key brain structures involved in the process is here provided. The input classification is performed through resonant neurons, stimulated by the complex dynamics generated in a lattice of recurrent spiking neurons modelling the Mushroom Bodies neuropile in the insect brain. The net…
Dynamic network identification from non-stationary vector autoregressive time series
2018
Learning the dynamics of complex systems features a large number of applications in data science. Graph-based modeling and inference underpins the most prominent family of approaches to learn complex dynamics due to their ability to capture the intrinsic sparsity of direct interactions in such systems. They also provide the user with interpretable graphs that unveil behavioral patterns and changes. To cope with the time-varying nature of interactions, this paper develops an estimation criterion and a solver to learn the parameters of a time-varying vector autoregressive model supported on a network of time series. The notion of local breakpoint is proposed to accommodate changes at individu…
Active monetary policy and instability in a phillips curve system
1998
The presence of nonlinearities in a Phillips curve system yields to complex dynamics, i.e., cyclical behavior that may (under some parametric set) become chaotic. This paper extends these conclusions by including an active monetary policy. We show how stabilization policy may lead to amplified instabilities and that agents' expectations tend to play a key role in the amount of these instabilities.
Cross-diffusion-induced subharmonic spatial resonances in a predator-prey system.
2018
In this paper we investigate the complex dynamics originated by a cross-diffusion-induced subharmonic destabilization of the fundamental subcritical Turing mode in a predator-prey reaction-diffusion system. The model we consider consists of a two-species Lotka-Volterra system with linear diffusion and a nonlinear cross-diffusion term in the predator equation. The taxis term in the search strategy of the predator is responsible for the onset of complex dynamics. In fact, our model does not exhibit any Hopf or wave instability, and on the basis of the linear analysis one should only expect stationary patterns; nevertheless, the presence of the nonlinear cross-diffusion term is able to induce …
Complex dynamics, hidden attractors and continuous approximation of a fractional-order hyperchaotic PWC system
2018
In this paper, a continuous approximation to studying a class of PWC systems of fractionalorder is presented. Some known results of set-valued analysis and differential inclusions are utilized. The example of a hyperchaotic PWC system of fractional order is analyzed. It is found that without equilibria, the system has hidden attractors.
Principled animation design improves comprehension of complex dynamics
2016
International audience; Learners can have difficulty in decomposing conventionally designed animations to obtain raw material suitable for building high quality mental models. A composition approach to designing animations based on the Animation Processing Model was developed as a principled alternative to prevailing approaches. Outcomes from studying novel and conventional animation designs (independent variable) were compared with respect to mental model quality, knowledge of local kinematics, and capacity to transfer (dependent variables). Study of a compositional animation that presented material in a contiguous fashion resulted in higher quality mental models of a piano mechanism than …