Fractional-order dynamics to study neuronal function

Coronel‐Escamilla, A.; Tuladhar, Rohisha; Stamova, Ivanka; Santamarı́a, Fidel

doi:10.1016/b978-0-32-390089-8.00020-9

Cited by 3 publications

(1 citation statement)

References 92 publications

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“…On the other hand, there is a mathematical area called fractional-order calculus (FOC) which has been gaining attention in recent years because it deals with derivatives and integrals of non-integer order [21]. FOC has been widely used to describe the behavior of different systems in applications such as electrical engineering, chemical engineering, control engineering, bioengineering, neuroscience, and so on [22,23]. The increasing interest in FOC in dynamical systems is because it has been demonstrated that FOC can model system properties that are intrinsically related to non-local behavior, such as the memory effect [24].…”

Section: Introductionmentioning

confidence: 99%

A Novel Fractional Multi-Order High-Gain Observer Design to Estimate Temperature in a Heat Exchange Process

Borja-Jaimes,

Adam-Medina,

García-Morales

et al. 2023

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In the present manuscript, we design a fractional multi-order high-gain observer to estimate temperature in a double pipe heat exchange process. For comparison purposes and since we want to prove that when using our novel technique, the estimation is more robust than the classical approach, we design a non-fractional high-gain observer, and then we compare the performance of both observers. We consider three scenarios: The first one considers the estimation of the system states by measuring only one output with no noise added on it and under ideal conditions. Second, we add noise to the measured output and then reconstruct the system states, and, third, in addition to the noise, we increase the gain parameter in both observers (non-fractional and fractional) due to the fact that we want to prove that the robustness changes in this parameter. The results showed that, using our approach, the estimated states can be recovered under noise circumstances in the measured output and under parameter change in the observer, contrary to using classical (non-fractional) observers where the states cannot be recovered. In all our tests, we used the normalized root-mean-square, integral square error, and integral absolute error indices, resulting in a better performance for our approach than that obtained using the classical approach. We concluded that our fractional multi-order high-gain observer is more robust to input noise than the classical high-gain observer.

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Section: Introductionmentioning

confidence: 99%

A Novel Fractional Multi-Order High-Gain Observer Design to Estimate Temperature in a Heat Exchange Process

Borja-Jaimes,

Adam-Medina,

García-Morales

et al. 2023

Axioms

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Diverse electrical responses in a network of fractional-order conductance-based excitable Morris-Lecar systems

Sharma

Mondal

Kaslik

et al. 2023

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The diverse excitabilities of cells often produce various spiking-bursting oscillations that are found in the neural system. We establish the ability of a fractional-order excitable neuron model with Caputo’s fractional derivative to analyze the effects of its dynamics on the spike train features observed in our results. The significance of this generalization relies on a theoretical framework of the model in which memory and hereditary properties are considered. Employing the fractional exponent, we first provide information about the variations in electrical activities. We deal with the 2D class I and class II excitable Morris-Lecar (M-L) neuron models that show the alternation of spiking and bursting features including MMOs & MMBOs of an uncoupled fractional-order neuron. We then extend the study with the 3D slow-fast M-L model in the fractional domain. The considered approach establishes a way to describe various characteristics similarities between fractional-order and classical integer-order dynamics. Using the stability and bifurcation analysis, we discuss different parameter spaces where the quiescent state emerges in uncoupled neurons. We show the characteristics consistent with the analytical results. Next, the Erdös-Rényi network of desynchronized mixed neurons (oscillatory and excitable) is constructed that is coupled through membrane voltage. It can generate complex firing activities where quiescent neurons start to fire. Furthermore, we have shown that increasing coupling can create cluster synchronization, and eventually it can enable the network to fire in unison. Based on cluster synchronization, we develop a reduced-order model which can capture the activities of the entire network. Our results reveal that the effect of fractional-order depends on the synaptic connectivity and the memory trace of the system. Additionally, the dynamics captures spike frequency adaptation and spike latency that occur over multiple timescales as the effects of fractional derivative, which has been observed in neural computation.

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Fractional order memcapacitive neuromorphic elements reproduce and predict neuronal function

Vazquez-Guerrero,

Tuladhar,

Psychalinos

et al. 2024

Sci Rep

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There is an increasing need to implement neuromorphic systems that are both energetically and computationally efficient. There is also great interest in using electric elements with memory, memelements, that can implement complex neuronal functions intrinsically. A feature not widely incorporated in neuromorphic systems is history-dependent action potential time adaptation which is widely seen in real cells. Previous theoretical work shows that power-law history dependent spike time adaptation, seen in several brain areas and species, can be modeled with fractional order differential equations. Here, we show that fractional order spiking neurons can be implemented using super-capacitors. The super-capacitors have fractional order derivative and memcapacitive properties. We implemented two circuits, a leaky integrate and fire and a Hodgkin–Huxley. Both circuits show power-law spiking time adaptation and optimal coding properties. The spiking dynamics reproduced previously published computer simulations. However, the fractional order Hodgkin–Huxley circuit showed novel dynamics consistent with criticality. We compared the responses of this circuit to recordings from neurons in the weakly-electric fish that have previously been shown to perform fractional order differentiation of their sensory input. The criticality seen in the circuit was confirmed in spontaneous recordings in the live fish. Furthermore, the circuit also predicted long-lasting stimulation that was also corroborated experimentally. Our work shows that fractional order memcapacitors provide intrinsic memory dependence that could allow implementation of computationally efficient neuromorphic devices. Memcapacitors are static elements that consume less energy than the most widely studied memristors, thus allowing the realization of energetically efficient neuromorphic devices.

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Fractional-order dynamics to study neuronal function

Cited by 3 publications

References 92 publications

A Novel Fractional Multi-Order High-Gain Observer Design to Estimate Temperature in a Heat Exchange Process

A Novel Fractional Multi-Order High-Gain Observer Design to Estimate Temperature in a Heat Exchange Process

Diverse electrical responses in a network of fractional-order conductance-based excitable Morris-Lecar systems

Fractional order memcapacitive neuromorphic elements reproduce and predict neuronal function

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