Related papers: Final state sensitivity and fractal basin boundari…
The synchronization stability of a complex network system of coupled phase oscillators is discussed. In case the network is affected by disturbances, a stochastic linearized system of the coupled phase oscillators may be used to determine…
Nonlinear systems possessing nonattracting chaotic sets, such as chaotic saddles, embedded in their state space may oscillate chaotically for a transient time before eventually transitioning into some stable attractor. We show that these…
The dynamical properties of a diluted fully-inhibitory network of pulse-coupled neurons are investigated. Depending on the coupling strength, two different phases can be observed. At low coupling the evolution rapidly converges towards…
Networks of strongly-coupled neurons with random connectivity exhibit chaotic, asynchronous fluctuations. In previous work, we showed that when endowed with an additional low-rank connectivity consisting of the outer product of orthogonal…
Hair cells of the auditory and vestibular systems display astonishing sensitivity, frequency selectivity, and temporal resolution to external signals. These specialized cells utilize an internal active amplifier to achieve highly sensitive…
We investigate the synchronization behavior and the emergence of chimera states in a system of two interacting populations of maps possessing chaotic neural-like dynamics. We characterize four collective states on the space of coupling…
Neural network models have recently demonstrated impressive prediction performance in complex systems where chaos and unpredictability appear. In spite of the research efforts carried out on predicting future trajectories or improving their…
The final-state interaction in multichannel decay processes is sytematically studied with application to B decay in mind. Since the final-state inteaction is intrinsically interwoven with the decay interaction in this case, no simple phase…
Neurons are often connected, spatially and temporally, in phenomenal ways that promote wave propagation. Therefore, it is essential to analyze the emergent spatiotemporal patterns to understand the working mechanism of brain activity,…
New fluctuation properties arise in problems where both spatial integration and energy summation are necessary ingredients. The quintessential example is given by the short-range approximation to the first order ground state contribution of…
We investigate the synchronization features of a network of spiking neurons under a distance-dependent coupling following a power-law model. The interplay between topology and coupling strength leads to the existence of different…
Multifractal dimensions allow for characterizing the localization properties of states in complex quantum systems. For ergodic states the finite-size versions of fractal dimensions converge to unity in the limit of large system size.…
In a manner similar to the molecular chaos that underlies the stable thermodynamics of gases, neuronal system may exhibit microscopic instability in individual neuronal dynamics while a macroscopic order of the entire population possibly…
We examine a simple biologically-motivated neural network, the three-layer version of the Chialvo-Bak `minibrain' [Neurosci. 90 (1999) 1137], and present numerical results which indicate that a non-equilibrium phase transition between…
Mesoscopic models of finite-size neuronal populations are crucial to understand the dynamics of neural networks in the brain, especially their fluctuations and response to stimuli. However, current theories to derive such models are based…
The periodic motion of a classical point particle in a one-dimensional double-well potential acquires a surprising degree of complexity if friction is added. Finite uncertainty in the initial state can make it impossible to predict in which…
The brain is a non-equilibrium system whose dynamics change in different brain states, such as wakefulness and deep sleep. Thermodynamics provides the tools for revealing these non-equilibrium dynamics. We used violations of the…
The onset of regular bursts in a group of irregularly bursting neurons with different individual properties is one of the most interesting dynamical properties found in neurobiological systems. In this paper we show how synchronization…
A diffusive system coupled to unequal boundary reservoirs reaches a non-equilibrium steady state. While the full-counting-statistics of current fluctuations in these states are well understood for generic systems, results for steady-state…
We investigate the equilibria of a random model network exhibiting extensive chaos. In this regime, a large number of equilibria is present. They are all saddles with low-dimensional unstable manifolds. Surprisingly, despite network's…