The application of nite-dimensional dynamical systems theory to non-Newtonian vortex ow indicates the presence of complex temporal dynamics that is attributed to shear thinning and normal stress (giving rise to the so-called Weissenberg rod climbing phenomenon). These aspects are examined for Rayleigh-Benard thermal convection and Taylor-Couette rotational ow, in an attempt to elucidate on the ...

In this report, we investigate phenomena on the edge of spatially uniform chaotic mode and spatial temporal chaos in a lattice of chaotic 1-D maps with only local connections. It is shown that in autonomous lattice with local connections, spatially uniform chaotic mode cannot exist if the Lyapunov exponent λ of the isolated chaotic map is greater than some critical value λcr > 0. We proposed a ...

We consider two neuronal networks coupled by long-range excitatory interactions. Oscillations in the gamma frequency band are generated within each network by local inhibition. When long-range excitation is weak, these oscillations phase lock with a phase shift dependent on the strength of local inhibition. Increasing the strength of long-range excitation induces a transition to chaos via perio...

We confront existing definitions of chaos with the state of the art in topological dynamics. The article does not propose any new definition of chaos but, starting from several topological properties that can be reasonably called chaotic, tries to sketch a theoretical view of chaos. Among the main ideas in this article are the distinction between overall chaos and partial chaos, and the fact th...

We study coupled map lattices with a scaling form of connectivity and show that the dynamics of these systems exhibit a transition from spatial disorder to spatially uniform, temporal chaos as the scaling is varied. We numerically investigate the eigenvalue spectrum of the random matrix characterizing fluctuations from spatial uniformity, and find that the spectrum is real, bounded, and has a g...

We discuss recent results obtained for the Hamiltonian Mean Field model. The model describes a system of N fully-coupled particles in one dimension and shows a second-order phase transition from a clustered phase to a homogeneous one when the energy is increased. Strong chaos is found in correspondence to the critical point on top of a weak chaotic regime which characterizes the motion at low e...

The aim of this article is twofold: (1). develop a strategy to prove the existence of chaos in weakly quasilinear systems, (2). strengthen the existing results on chaos in partial differential equations. First, we study a sineGordon equation containing weakly quasilinear terms, and existence of chaos is proved. Then, we study a Ginzburg-Landau equation containing weakly quasilinear terms, and e...

Recent discovery of the massive presence of gap junction couplings among neocortical FS (and LTS) interneurons poses serious questions about their collective dynamical behavior, and their possible cognitive roles. We present here the theoretical possibility that a class of neurons coupled by gap junctions may emerge spatio-temporal chaos itinerant among attractors in Milnor’s sense, which in tu...

In this paper, a recurrent spiking neural networks is trained on an robot to learn to avoid obstacles using visual flow. At the starting of the process, this network is initialized in a ”chaotic” state and a STDP-like learning algorithm is used. We argue that a proper scaling variable can direct the network from chaos to synchronized state and back. This process allows us to train the robot bec...

Multistable perception is perception in which two (or more) interpretations of the same ambiguous image alternate while an obserber looks at them. Perception undergoes involuntary and random-like change. The question arises whether the apparent randomness of alternation is real (that is, due to a stochastic process) or whether any underlying deterministic structure to it exists. In this paper, ...