Dynamics and implementation techniques of fractional-order neuron models: a survey

2022 ◽  
pp. 483-511
Author(s):  
Mohammad Rafiq Dar ◽  
Nasir Ali Kant ◽  
Farooq Ahmad Khanday
Keyword(s):  
Fractional Order ◽  
Neuron Models ◽  
Implementation Techniques ◽  
Order Neuron

FPGA Realization of Fractional Order Neuron

2020 ◽  
Vol 81 ◽  
pp. 372-385 ◽  
Author(s):  
S.A. Malik ◽  
A.H. Mir
Keyword(s):  
Fractional Order ◽  
Order Neuron

scholarly journals Firing activities of a fractional-order FitzHugh-Rinzel bursting neuron model and its coupled dynamics

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Argha Mondal ◽  
Sanjeev Kumar Sharma ◽  
Ranjit Kumar Upadhyay ◽  
Arnab Mondal
Keyword(s):  
Fractional Order ◽  
Complex Dynamics ◽  
Firing Frequency ◽  
Order System ◽  
Neuron Models ◽  
Order Model ◽  
Constant Input ◽  
Wide Range ◽  
Excitable Systems ◽  
Firing Properties

Abstract Fractional-order dynamics of excitable systems can be physically described as a memory dependent phenomenon. It can produce diverse and fascinating oscillatory patterns for certain types of neuron models. To address these characteristics, we consider a nonlinear fast-slow FitzHugh-Rinzel (FH-R) model that exhibits elliptic bursting at a fixed set of parameters with a constant input current. The generalization of this classical order model provides a wide range of neuronal responses (regular spiking, fast-spiking, bursting, mixed-mode oscillations, etc.) in understanding the single neuron dynamics. So far, it is not completely understood to what extent the fractional-order dynamics may redesign the firing properties of excitable systems. We investigate how the classical order system changes its complex dynamics and how the bursting changes to different oscillations with stability and bifurcation analysis depending on the fractional exponent (0 < α ≤ 1). This occurs due to the memory trace of the fractional-order dynamics. The firing frequency of the fractional-order FH-R model is less than the classical order model, although the first spike latency exists there. Further, we investigate the responses of coupled FH-R neurons with small coupling strengths that synchronize at specific fractional-orders. The interesting dynamical characteristics suggest various neurocomputational features that can be induced in this fractional-order system which enriches the functional neuronal mechanisms.

Current Stimuli That Provide Membrane Voltage Tracking in a Six Dimensional Neuron Model

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Melinda E. Koelling ◽  
Damon A. Miller ◽  
Michael Ellinger ◽  
Frank L. Severance ◽  
John Stahl
Keyword(s):  
Optimal Control ◽  
Neuron Model ◽  
Optimization Techniques ◽  
Reference Voltage ◽  
Membrane Voltage ◽  
Neuron Models ◽  
Input Stimulus ◽  
Optimal Input ◽  
Stimulus Current ◽  
Order Neuron

Optimization techniques have been applied to neuron models for a variety of purposes, including control of neuron firing rates and minimizing input stimulus current magnitudes. Optimal control is used to minimize a quantity of interest; often, the time or energy needed to complete an objective. Rather than attempting to control or modify neuron dynamics, this paper demonstrates that optimal control can be used to obtain an optimal input stimulus current i*(t) which causes a six dimensional Hodgkin–Huxley type neuron model to approximate a specified reference membrane voltage. The reference voltages considered in this paper consist of one or more action potentials as evoked by an input current i(t). In the described method, the user prescribes a balance of low squared integral of input stimulus current (input stimulus “energy”) and accurate tracking of the original reference voltage. In a previous work, the authors applied this approach to a reduced order neuron model. This paper demonstrates the applicability of this technique to biologically plausible higher dimensional conductance based neuron models. For each investigated neuron response, the method discovered optimal input stimuli current i*(t) having a lower energy than the original i(t), while still providing accurate tracking of the reference voltage.

Fractional Derivatives and Complex Modes of Vibration

2009 ◽  
Author(s):  
Masaharu Kuroda
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Degrees Of Freedom ◽  
Fractional Derivatives ◽  
Vibratory System ◽  
Signal Conversion ◽  
Additional Signal ◽  
Complex Modes ◽  
Implementation Techniques ◽  
Modes Of Vibration

As described herein, we develop a method to obtain a fractional derivative response of a vibratory system with multiple degrees of freedom (DOF). To obtain fractional-order derivatives/integrals of dynamic response at a certain point on a structure presents technical difficulties because measurements of fractional-order derivative/integral responses in structural dynamics yield some implementation techniques. However, our method obviates special sensors with additional signal-conversion functions. Therefore, existing displacement and velocity sensors can work. Obtaining fractional derivative responses can be accomplished using three methods. Using any of the three methods, fractional states can be expressed with complex vibration modes, in which each point of the system oscillates with a phase that is different from “in-phase” or “out-of-phase.”

scholarly journals SUPPRESSING SPIRAL WAVE TURBULENCE IN A SIMPLE FRACTIONAL-ORDER DISCRETE NEURON MAP USING IMPULSE TRIGGERING

Fractals ◽  
2021 ◽  
pp. 2140030
Author(s):  
KARTHIKEYAN RAJAGOPAL ◽  
SHIRIN PANAHI ◽  
MO CHEN ◽  
SAJAD JAFARI ◽  
BOCHENG BAO
Keyword(s):  
Fractional Order ◽  
Neuron Model ◽  
Spiral Wave ◽  
Wave Turbulence ◽  
Effective Parameters ◽  
Neuron Models ◽  
Collective Behaviors ◽  
One Dimensional ◽  
Dynamical Characteristics ◽  
Significant Interest

One-dimensional (1D) map-based neuron models are of significant interest according to their simplicity of simulation and ability to mimic real neurons’ complex behaviors. A fractional-order 1D neuron map is proposed in this paper. Dynamical characteristics of the model are analyzed by obtaining bifurcation diagrams and the Lyapunov exponents’ diagram. Furthermore, emerging the spiral wave as one of the most important collective behaviors is studied in a 2D lattice consisting of this new FO neuron model. The outcome of changing stimuli, coupling strength, and fractional-order parameter as the effective parameters is examined in this network. Moreover, an efficient way of suppressing the spiral wave has been investigated using impulse triggering.

Tuning and implementation methods for fractional-order controllers

2012 ◽  
Vol 15 (2) ◽  
Author(s):  
Ivo Petráš
Keyword(s):  
Fractional Order ◽  
Pid Controllers ◽  
Fir Filters ◽  
Practical Implementation ◽  
Approximation Methods ◽  
Programmable Logic ◽  
Survey Paper ◽  
Implementation Techniques ◽  
Self Tuning ◽  
Tuning Methods

AbstractThis survey paper presents methods of tuning and implementation of Fractional-Order Controllers (FOC). In the article are presented tuning, auto-tuning and self-tuning methods for the FOC. As the FOC are considered fractional PID controllers, the Commande Robuste d’Ordre Non Entier (CRONE) controller and fractional-order lead-lag compensators. As implementation techniques are described the IIR and FIR filters forms of approximation methods, which can be easily implemented in microprocessor devices such as for example the Programmable Logic Controller (PLC), etc. The possibility for analogue implementation of such kind of controllers is also mentioned. An example of practical implementation of the FOC together with all problems and restrictions are described as well.

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