An analog simulation of non-integer, order transfer functions for analysis of electrode ppocesses

Ichise, Mitsunojo

doi:10.1016/0368-1874(71)80037-0

Cited by 19 publications

(15 citation statements)

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“…The transformation of an integer-order model into a fractional-order model needs to be precise as to the order of differentiation α: a small change in α may cause a big change in the final results [14]. FDEs can be used to model certain phenomena which cannot be adequately modeled by IDEs [15]. FDEs are commonly used on biological systems since they are related in a natural way to systems with memory.…”

Section: Introductionmentioning

confidence: 99%

Bifurcations and chaos in a discrete SI epidemic model with fractional order

et al. 2018

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In this study, a new discrete SI epidemic model is proposed and established from SI fractional-order epidemic model. The existence conditions, the stability of the equilibrium points and the occurrence of bifurcation are analyzed. By using the center manifold theorem and bifurcation theory, it is shown that the model undergoes flip and Neimark-Sacker bifurcation. The effects of step size and fractional-order parameters on the dynamics of the model are studied. The bifurcation analysis is also conducted and our numerical results are in agreement with theoretical results.

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Section: Introductionmentioning

confidence: 99%

Bifurcations and chaos in a discrete SI epidemic model with fractional order

et al. 2018

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“…Fractional-order calculus fractional differential systems are an interesting subject among mathematicians, physicists, and also engineers [1]- [3]. Moreover, we can find a great number of applications in science and engineering, such as electromagnetic waves [4], electrodeelectrolyte polarization [5], dielectric polarization [6], viscoelastic systems [7], heat conduction [8], neural networks [9], and so on. The fractional-order derivative is an excellent tool, making a real object models more accurately than the integer order.…”

Section: Introductionmentioning

confidence: 99%

Existence and Uniform Stability Analysis of Fractional-Order Complex-Valued Neural Networks With Time Delays

Rakkiyappan

Cao

Velmurugan

2015

IEEE Trans. Neural Netw. Learning Syst.

259

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This paper deals with the problem of existence and uniform stability analysis of fractional-order complex-valued neural networks with constant time delays. Complex-valued recurrent neural networks is an extension of real-valued recurrent neural networks that includes complex-valued states, connection weights, or activation functions. This paper explains sufficient condition for the existence and uniform stability analysis of such networks. Three numerical simulations are delineated to substantiate the effectiveness of the theoretical results.

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“…It has been found that with the help of fractional calculus, many systems in interdisciplinary fields can be described OPEN ACCESS more accurately, such as viscoelastic systems [1], dielectric polarization [2], electrode-electrolyte polarization [3], finance systems and electromagnetic waves [4]. That is to say, fractional calculus provides a superb instrument for the description of the memory and hereditary properties of various materials and processes.…”

Section: Introductionmentioning

confidence: 99%

Robust Control of a Class of Uncertain Fractional-Order Chaotic Systems with Input Nonlinearity via an Adaptive Sliding Mode Technique

Tian

Fei

2014

Entropy

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Abstract:In this paper, the problem of stabilizing a class of fractional-order chaotic systems with sector and dead-zone nonlinear inputs is investigated. The effects of model uncertainties and external disturbances are fully taken into account. Moreover, the bounds of both model uncertainties and external disturbances are assumed to be unknown in advance. To deal with the system's nonlinear items and unknown bounded uncertainties, an adaptive fractional-order sliding mode (AFSM) controller is designed. Then, Lyapunov's stability theory is used to prove the stability of the designed control scheme. Finally, two simulation examples are given to verify the effectiveness and robustness of the proposed control approach.

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An analog simulation of non-integer, order transfer functions for analysis of electrode ppocesses

Cited by 19 publications

References 0 publications

Bifurcations and chaos in a discrete SI epidemic model with fractional order

Bifurcations and chaos in a discrete SI epidemic model with fractional order

Existence and Uniform Stability Analysis of Fractional-Order Complex-Valued Neural Networks With Time Delays

Robust Control of a Class of Uncertain Fractional-Order Chaotic Systems with Input Nonlinearity via an Adaptive Sliding Mode Technique

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