Fractional Differential Equations

Neuromorphic computing has come to refer to a variety of brain-inspired computers, devices, and models that contrast the pervasive von Neumann computer architecture This biologically inspired approach has created highly connected synthetic neurons and synapses that can be used to model neuroscience theories as well as solve challenging machine learning problems The promise of the technology is to create a brain-like ability to learn and adapt, but the technical challenges are significant, starting with an accurate neuroscience model of how the brain works, to finding materials and engineering breakthroughs to build devices to support these models, to creating a programming framework so the systems can learn, to creating applications with brain-like capabilities In this work, we provide a comprehensive survey of the research and motivations for neuromorphic computing over its history We begin with a 35-year review of the motivations and drivers of neuromorphic computing, then look at the major research areas of the field, which we define as neuro-inspired models, algorithms and learning approaches, hardware and devices, supporting systems, and finally applications We conclude with a broad discussion on the major research topics that need to be addressed in the coming years to see the promise of neuromorphic computing fulfilled The goals of this work are to provide an exhaustive review of the research conducted in neuromorphic computing since the inception of the term, and to motivate further work by illuminating gaps in the field where new research is needed

A Survey of Neuromorphic Computing and Neural Networks in Hardware.

Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks

This paper constructs a new hyperchaotic system based on Lu system by using a state feedback controller. The detailed dynamical behaviors of this hyperchaotic system are further investigated, including Lyapunov exponents spectrum, bifurcation, and Poincare mapping. Moreover, a novel circuit diagram is designed for verifying the hyperchaotic behaviors and some experimental observations are also given.

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Generating hyperchaotic Lü attractor via state feedback control

Backstepping control is effective for integer-order nonlinear systems with triangular structures. Nevertheless, it is hard to be applied to fractional-order nonlinear systems as the fractional-order derivative of a compound function is very complicated. In this paper, we develop an adaptive fuzzy backstepping control method for a class of uncertain fractional-order nonlinear systems with unknown external disturbances. In each step, a complicated unknown nonlinear function produced by differentiating a compound function with a fractional order is approximated by a fuzzy logic system, and a virtual control law is designed based on the fractional Lyapunov stability criterion. At the last step, an adaptive fuzzy controller that ensures convergence of the tracking error is constructed. The effectiveness of the proposed method has been verified by two simulation examples.

Adaptive Fuzzy Backstepping Control of Fractional-Order Nonlinear Systems

In this letter, a simple nonlinear state feedback controller is designed for generating hyperchaos from a three-dimensional autonomous chaotic system. The hyperchaotic system is not only demonstrated by computer simulations but also verified with bifurcation analysis, and is implemented experimentally via an electronic circuit.

Generating hyperchaos via state feedback control

In this paper, the problems of stability and Hopf bifurcation in a class of fractional-order complex-valued single neuron model with time delay are addressed. With the help of the stability theory ...

Stability and Hopf Bifurcation of Fractional-Order Complex-Valued Single Neuron Model with Time Delay

Chaos and hyperchaos in fractional-order cellular neural networks

Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays

SUMMARY In this letter, a new hyperchaotic system is formulated by introducing an additional state into the third-order generalized Lorenz equation The existence of the hyperchaos is veried with bifurcation analysis, and the bifurcation routes from periodic, quasi-periodic, chaotic and hyperchaotic evolutions are observed Various attractors are illustrated not only by computer simulation but also by the realization of an electronic circuit Copyright ? 2005 John Wiley & Sons, Ltd

Yuxia Li

Papers

Generating hyperchaos via state feedback control

Stability and Hopf Bifurcation of Fractional-Order Complex-Valued Single Neuron Model with Time Delay

Chaos and hyperchaos in fractional-order cellular neural networks

Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays

Hyperchaos evolved from the generalized Lorenz equation