Van der Pol oscillator based on NbO2 volatile memristor: A simulation analysis

Luo, Ziqing; Bo, Yeheng; Sadaf, Sharif Md.; Liu, Xinjun

doi:10.1063/5.0073285

“…11 (b), (c), (d)). For example, leaky-integrated-firing of a biological neuron can be technically realized by van der Pol (vdP) oscillators (van der Pol, 1926;Pikovskij et al, 2003;Ignatov et al, 2016), compact devices based on VO 2 or NbO x , which exhibit a negative differential resistance (NDR) I-V curve (D. Lee et al, 2018;Maffezzoni et al, 2015;Driscoll et al, 2012;Luo et al, 2022), or integrated, mixed-signal circuits (X. Cheng et al, 2021).…”

Section: Artificial Spatio-temporal Networkmentioning

confidence: 99%

Matter & Mind Matter

Birkoben¹,

Kohlstedt²

2022

Preprint

1

0

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As a result of a hundred million years of evolution, living animals have adapted extremely well to their ecological niche. Such adaptation implies species-specific interactions with their immediate environment by processing sensory cues and responding with appropriate behavior. Understanding how living creatures perform pattern recognition and cognitive tasks is of particular importance for computing architectures: by studying these information pathways refined over eons of evolution, researchers may be able to streamline the process of developing more highly advanced, energy efficient autonomous systems. With the advent of novel electronic and ionic components along with a deeper understanding of information pathways in living species, a plethora of opportunities to develop completely novel information processing avenues are within reach. Here, we describe the basal information pathways in nervous systems, from the local neuron level to the entire nervous system network. The dual importance of local learning rules is addressed, from spike timing dependent plasticity at the neuron level to the interwoven morphological and dynamical mechanisms of the global network. Basal biological principles are highlighted, including phylogenies, ontogenesis, and homeostasis, with particular emphasis on network topology and dynamics. While in machine learning system training is performed on virgin networks without any a priori knowledge, the approach proposed here distinguishes itself unambiguously by employing growth mechanisms as a guideline to design novel computing architectures. Including fundamental biological information pathways that explore the spatiotemporal fundamentals of nervous systems has untapped potential for the development of entirely novel information processing systems. Finally, a benchmark for neuromorphic systems is suggested.

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“…However, apart from the dynamical system, the Mathieu Equation is also linked to other subjects, such as applied and computational mathematics [28] and many engineering fields [29], due to the wide variety of its uses and the methods needed for qualitatively analyzing it. The Van der Pol equation, however, finds applications in many different industries like electronics, communication systems, and biological systems because of its capacity to record intricate dynamics [30].…”

Section: Introductionmentioning

confidence: 99%

Oscillator Simulation with Deep Neural Networks

Rahman,

Danish,

Lu

2024

Mathematics

1

0

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The motivation behind this study is to overcome the complex mathematical formulation and time-consuming nature of traditional numerical methods used in solving differential equations. It seeks an alternative approach for more efficient and simplified solutions. A Deep Neural Network (DNN) is utilized to understand the intricate correlations between the oscillator’s variables and to precisely capture their dynamics by being trained on a dataset of known oscillator behaviors. In this work, we discuss the main challenge of predicting the behavior of oscillators without depending on complex strategies or time-consuming simulations. The present work proposes a favorable modified form of neural structure to improve the strategy for simulating linear and nonlinear harmonic oscillators from mechanical systems by formulating an ANN as a DNN via an appropriate oscillating activation function. The proposed methodology provides the solutions of linear and nonlinear differential equations (DEs) in differentiable form and is a more accurate approximation as compared to the traditional numerical method. The Van der Pol equation with parametric damping and the Mathieu equation are adopted as illustrations. Experimental analysis shows that our proposed scheme outperforms other numerical methods in terms of accuracy and computational cost. We provide a comparative analysis of the outcomes obtained through our proposed approach and those derived from the LSODA algorithm, utilizing numerical techniques, Adams–Bashforth, and the Backward Differentiation Formula (BDF). The results of this research provide insightful information for engineering applications, facilitating improvements in energy efficiency, and scientific innovation.

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Matter and Mind Matter

Birkoben,

Kohlstedt

2023

Springer Series on Bio- And Neurosystems

0

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As a result of a hundred million years of evolution, living animals have adapted extremely well to their ecological niche. Such adaptation implies species-specific interactions with their immediate environment by processing sensory cues and responding with appropriate behavior. Understanding how living creatures perform pattern recognition and cognitive tasks is of particular importance for computing architectures: by studying these information pathways refined over eons of evolution, researchers may be able to streamline the process of developing more highly advanced, energy efficient autonomous systems. With the advent of novel electronic and ionic components along with a deeper understanding of information pathways in living species, a plethora of opportunities to develop completely novel information processing avenues are within reach. Here, we describe the basal information pathways in nervous systems, from the local neuron level to the entire nervous system network. The dual importance of local learning rules is addressed, from spike timing dependent plasticity at the neuron level to the interwoven morphological and dynamical mechanisms of the global network. Basal biological principles are highlighted, including phylogenies, ontogenesis, and homeostasis, with particular emphasis on network topology and dynamics. While in machine learning system training is performed on virgin networks without any a priori knowledge, the approach proposed here distinguishes itself unambiguously by employing growth mechanisms as a guideline to design novel computing architectures. Including fundamental biological information pathways that explore the spatiotemporal fundamentals of nervous systems has untapped potential for the development of entirely novel information processing systems. Finally, a benchmark for neuromorphic systems is suggested.

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Van der Pol oscillator based on NbO2 volatile memristor: A simulation analysis

Cited by 4 publications

References 30 publications

Matter & Mind Matter

Matter & Mind Matter

Oscillator Simulation with Deep Neural Networks

Matter and Mind Matter

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