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A classical view of neural computation is that it can be characterized in terms of convergence to attractor states or sequential transitions among states in a noisy background. After over three decades, is this still a valid model of how brain dynamics implements cognition? This book provides a comprehensive collection of recent theoretical and experimental contributions addressing the question of stable versus transient neural population dynamics from complementary angles. These studies showcase recent efforts for designing a framework that encompasses the multiple facets of metastability in neural responses, one of the most exciting topics currently in systems and computational neuroscience.

Attractor Dynamics --- Trial-to-trial Variability --- Transient Dynamics --- Neural Noise --- Metastability

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A classical view of neural computation is that it can be characterized in terms of convergence to attractor states or sequential transitions among states in a noisy background. After over three decades, is this still a valid model of how brain dynamics implements cognition? This book provides a comprehensive collection of recent theoretical and experimental contributions addressing the question of stable versus transient neural population dynamics from complementary angles. These studies showcase recent efforts for designing a framework that encompasses the multiple facets of metastability in neural responses, one of the most exciting topics currently in systems and computational neuroscience.

Attractor Dynamics --- Trial-to-trial Variability --- Transient Dynamics --- Neural Noise --- Metastability

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This book is a series of case studies with a common theme. Some refer closely to previous work by the author, but contrast with how they have been treated before, and some are new. Comparisons are drawn using various sorts of psychological and psychophysiological data that characteristically are particularly nonlinear, non-stationary, far from equilibrium and even chaotic, exhibiting abrupt transitions that are both reversible and irreversible, and failing to meet metric properties. A core idea is that both the human organism and the data analysis procedures used are filters, that may variously preserve, transform, distort or even destroy information of significance.

Physical Sciences & Mathematics --- Sciences - General --- Chaotic behavior in systems --- Time-series analysis --- Mathematical models. --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Differentiable dynamical systems --- Dynamics --- Nonlinear theories --- System theory --- reliability --- psychological tests --- psychometrics --- human being --- classification --- case study --- Attractor --- Eigenvalues and eigenvectors --- Markov chain --- Stationary process --- Time series

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Recent research in the fields related to the quantum information theory (QIT) is becoming some of the most intriguing and promising investigations in contemporary physics. Many novel QIT concepts are discussed in the literature, and the broad range of new models of quantum optics and solid-state physics have been recently considered in the context of QIT. Theideas of symmetry are widely discussed in all physical sciences, becoming keystones of various concepts and considerations, leading to novel discoveries in physics. Thus, this Special Issue is devoted to the broad range of QIT topics that are related to the ideas of symmetry. It covers a broad range of ideas that can develop upon the basic research and applications in the field of quantum information, and in general, quantum theory.

s–wave symmetry Eliashberg formalism --- BaGe3 superconductor --- thermodynamic properties --- nonlinearly coupled oscillators --- PT symmetry --- cross-Kerr nonlinearity --- stability analysis --- quantum properties --- nonlinear oscillator --- quantum entanglement --- open system --- ??-symmetry --- entanglement --- negativity --- quantum control --- Mathieu functions --- time-dependent driving fields --- superconductivity --- four-fermion attraction --- Meissner effect --- fermion quartets --- attractor --- complex Ginzburg–Landau equation --- soliton --- quantum machine learning --- associative memory

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In recent years, entropy has been used as a measure of the degree of chaos in dynamical systems. Thus, it is important to study entropy in nonlinear systems. Moreover, there has been increasing interest in the last few years regarding the novel classification of nonlinear dynamical systems including two kinds of attractors: self-excited attractors and hidden attractors. The localization of self-excited attractors by applying a standard computational procedure is straightforward. In systems with hidden attractors, however, a specific computational procedure must be developed, since equilibrium points do not help in the localization of hidden attractors. Some examples of this kind of system are chaotic dynamical systems with no equilibrium points; with only stable equilibria, curves of equilibria, and surfaces of equilibria; and with non-hyperbolic equilibria. There is evidence that hidden attractors play a vital role in various fields ranging from phase-locked loops, oscillators, describing convective fluid motion, drilling systems, information theory, cryptography, and multilevel DC/DC converters. This Special Issue is a collection of the latest scientific trends on the advanced topics of dynamics, entropy, fractional order calculus, and applications in complex systems with self-excited attractors and hidden attractors.

S-Box algorithm --- empirical mode decomposition --- service game --- existence --- hyperchaotic system --- static memory --- complex-variable chaotic system --- neural network --- fractional-order --- permutation entropy --- adaptive approximator-based control --- BOPS --- Bogdanov Map --- complex systems --- Thurston’s algorithm --- parameter estimation --- fractional discrete chaos --- full state hybrid projective synchronization --- self-excited attractor --- stability --- PRNG --- inverse full state hybrid projective synchronization --- entropy measure --- chaos --- chaotic flow --- multistable --- core entropy --- multiscale multivariate entropy --- multistability --- new chaotic system --- strange attractors --- chaotic systems --- spatial dynamics --- spectral entropy --- resonator --- stochastic (strong) entropy solution --- multichannel supply chain --- Hubbard tree --- approximate entropy --- circuit design --- coexistence --- sample entropy --- chaotic maps --- chaotic map --- Gaussian mixture model --- entropy --- laser --- Non-equilibrium four-dimensional chaotic system --- multiple attractors --- projective synchronization --- hidden attractors --- hidden attractor --- chaotic system --- entropy analysis --- self-excited attractors --- multiple-valued --- self-reproducing system --- implementation --- unknown complex parameters --- optimization methods --- image encryption --- generalized synchronization --- uncertain dynamics --- fractional order --- nonlinear transport equation --- external rays --- Lyapunov exponents --- inverse generalized synchronization --- fixed point --- uniqueness --- electronic circuit realization --- synchronization --- Hopf bifurcation