529 research outputs found

    Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

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    This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

    Entropy in Dynamic Systems

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    In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and non-uniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed

    A switching control for finite-time synchronization of memristor-based BAM neural networks with stochastic disturbances

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    This paper deals with the finite-time stochastic synchronization for a class of memristorbased bidirectional associative memory neural networks (MBAMNNs) with time-varying delays and stochastic disturbances. Firstly, based on the physical property of memristor and the circuit of MBAMNNs, a MBAMNNs model with more reasonable switching conditions is established. Then, based on the theory of Filippov’s solution, by using Lyapunov–Krasovskii functionals and stochastic analysis technique, a sufficient condition is given to ensure the finite-time stochastic synchronization of MBAMNNs with a certain controller. Next, by a further discussion, an errordependent switching controller is given to shorten the stochastic settling time. Finally, numerical simulations are carried out to illustrate the effectiveness of theoretical results

    Bifurcation and Chaos in Fractional-Order Systems

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    This book presents a collection of seven technical papers on fractional-order complex systems, especially chaotic systems with hidden attractors and symmetries, in the research front of the field, which will be beneficial for scientific researchers, graduate students, and technical professionals to study and apply. It is also suitable for teaching lectures and for seminars to use as a reference on related topics

    Predicting catastrophes: the role of criticality

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    Is prediction feasible in systems at criticality? While conventional scale-invariant arguments suggest a negative answer, evidence from simulation of driven-dissipative systems and real systems such as ruptures in material and crashes in the financial market have suggested otherwise. In this dissertation, I address the question of predictability at criticality by investigating two non-equilibrium systems: a driven-dissipative system called the OFC model which is used to describe earthquakes and damage spreading in the Ising model. Both systems display a phase transition at the critical point. By using machine learning, I show that in the OFC model, scaling events are indistinguishable from one another and only the large, non-scaling events are distinguishable from the small, scaling events. I also show that as the critical point is approached, predictability falls. For damage spreading in the Ising model, the opposite behavior is seen: the accuracy of predicting whether damage will spread or heal increases as the critical point is approached. I will also use machine learning to understand what are the useful precursors to the prediction problem
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