نوع مقاله: مقاله کامل پژوهشی

نویسندگان

1 دانشجوی دکتری مهندسی پزشکی، گروه بیوالکتریک، دانشکده‌ی مهندسی پزشکی، دانشگاه صنعتی امیرکبیر، تهران، ایران

2 استادیار، گروه بیوالکتریک، دانشکده‌ی مهندسی پزشکی، دانشگاه صنعتی امیرکبیر، تهران، ایران

چکیده

موج‌های مارپیچی نوع خاصی از الگوهای زمانی-مکانی هستند که در بسیاری از سیستم‌های پیچیده از جمله شبکه‌های نورونی وجود دارند. ظهور این امواج به ساختار شبکه و هم‌چنین دینامیک اجزای تشکیل دهنده‌ی آن بستگی دارد. در این مقاله، ابتدا یک مدل نورونی جدید بر پایه‌ی مدل هیندمارش-رز ارائه شده است. در این مدل از یک تابع ممریستوری هیپربولیک به عنوان شار مغناطیسی نورون استفاده شده که خاصیت مشتق‌پذیری به طور یک‌نواخت را دارد. هم‌چنین یک القای الکترومغناطیسی خارجی نیز به نورون وارد شده و مدل نورونی با رسم نمودار بایفورکیشن و طیف لیاپانوف، در دو حالت بدون القای خارجی و با القای متناوب مورد بررسی قرار گرفته است. نمودار بایفورکیشن مدل پیشنهادی، خاصیت ضدیک‌نواختی را نشان داده که در مدل‌های پیشین مشاهده نشده است. سپس یک شبکه‌ی مربعی از مدل نورونی جدید در نظر گرفته شده و الگوهای مکانی-زمانی مورد بررسی قرار گرفته‌اند. موج‌های مارپیچی، با تغییر پارامترها در محدوده‌هایی معین قابل مشاهده بوده و شکل‌گیری این امواج به تعامل بین تمام پارامترها وابسته است.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Spiral Waves Formation in a Network of Neuron Model with Monotonically Differentiable Magnetic Flux

نویسندگان [English]

  • Fatemeh Parastesh 1
  • Sajad Jafari 2
  • Hamed Azarnoush 2

1 Ph.D. Student, Bioelectric Department, Biomedical Engineering Faculty, Amirkabir University of Technology, Tehran, Iran

2 Assistant Professor, Bioelectric Department, Biomedical Engineering Faculty, Amirkabir University of Technology, Tehran, Iran

چکیده [English]

Spiral wave is a particular spatiotemporal pattern, observed in a wide range of complex systems such as neuronal network. Appearance of these waves is related to the network structure as well as the dynamics of its blocks. In this paper, we propose a new modified Hindmarsh-Rose neuron model. The proposed model uses a hyperbolic memductance function as the monotonically differentiable magnetic flux. An external electromagnetic excitation is also considered in the model. Firstly, we study the dynamics of the proposed neuron model through bifurcation diagram and Lyapunov spectrum, in two cases of no excitation and periodic excitation. The bifurcation diagram shows the property of antimonotonicity, which has not been observed in the previous models. Then a square network is constructed and we investigate the spatiotemporal pattrens. By varying the parameters values, spiral waves are observed in specific ranges. The formation of these waves depends on the interaction of all parameters simultaneously. 

کلیدواژه‌ها [English]

  • modified Hindmarsh-Rose neuron model
  • neuronal network
  • spiral waves

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