FPGA Realization of Fractional Order Neuron

• Published in: Applied Mathematical Modelling 2020-05, Vol.81, p.372-385
• Main Authors: Malik, S.A., Mir, A.H.
• Format: Article
• Language: English
• Subjects: Circuits; Computational neuroscience; Dynamic characteristics; Field programmable gate arrays; Field-programmable-gate-arrays (FPGA); Fractional calculus; Fractional Hindmarsh Rose neuron (HR); Fractional-operator; Hardware; Integers; Low voltage; Mathematical models; Neurons; Operators (mathematics); Order parameters; Power management; Synchronism; Synchronization
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2019.12.008

•Fractional order neuron depicts several dynamical behaviors even for the same stimulus.•There is a trade-off between accuracy and hardware cost in fractional operator.•The synchronization between fractional neurons increases as the coupling factor value increases.•Fractional operator depicts better memory characteristics compared to integer order. In this paper fractional Hindmarsh Rose (HR) neuron, which mimics several behaviors of a real biological neuron is implemented on field programmable gate array (FPGA). The results show several differences in the dynamic characteristics of integer and fractional order Hindmarsh Rose neuron models. The integer order model shows only one type of firing characteristics when the parameters of model remains same. The fractional order model depicts several dynamical behaviors even for the same parameters as the order of the fractional operator is varied. The firing frequency increases when the order of the fractional operator decreases. The fractional order is therefore key in determining the firing characteristics of biological neurons. To implement this neuron model first the digital realization of different fractional operator approximations are obtained, then the fractional integrator is used to obtain the low power and low cost hardware realization of fractional HR neuron. The fractional neuron model has been implemented on a low voltage and low power circuit and then compared with its integer counter part. The hardware is used to demonstrate the different dynamical behaviors of fractional HR neuron for different type of approximations obtained for fractional operator in this paper. A coupled network of fractional order HR neurons is also implemented. The results also show that synchronization between neurons increases as long as coupling factor keeps on increasing.