بررسی پایداری شبکه عصبی BAM تاخیری دولایه براساس پارامترهای شبکه

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکترا، گروه ریاضی، دانشکده علوم ریاضی و آمار، پردیس علوم پایه، دانشگاه بیرجند، ایران

2 استادیار، گروه ریاضی، دانشکده علوم ریاضی و آمار، پردیس علوم پایه، دانشگاه بیرجند، ایران

3 استا‌د، گروه برق، دانشکده مهندسی، دانشگاه ویسکانسین-پلتویل، آمریکا

4 دانشیار، گروه ریاضی، دانشکده علوم ریاضی و آمار، پردیس علوم پایه، دانشگاه بیرجند، ایران

چکیده

در این مقاله پایداری شبکه عصبی- تاخیری بم متشکل از دو لایه بررسی می‌شود. برای این کار بعد از خطی‌سازی شبکه عصبی بم به بررسی معادله مشخصه پرداخته و با توجه به حقیقی یا مختلط بودن ریشه‌های ماتریس اتصالات شرایطی به‌دست می‌آوریم تا سیستم اصلی دارای مقادیر ویژه با قسمت حقیقی مخالف صفر داشته باشد. با توجه به قضیه هارتمن-گروبمن ساختار کیفی سیستم با ساختار خطی آن یکسان است. بنابراین با توجه به حالات مقادیر ویژه ماتریس اتصال در چندجمله‌ای مشخصه، کرانی برای پارامترهای شبکه به‌دست می‌آوریم. که با توجه به شرایط به‌دست آمده، پایداری را تعریف می‌کنیم. نتایج نشان می‌دهد، زمانی که مقادیر ویژه دارای قسمت حقیقی منفی باشد، شبکه عصبی به پایداری مجانبی می‌رسد. همچنین به اثرگذاری تاخیر در ایجاد نوسان در شبکه عصبی بم نیز پرداخته شده و پارامتری برای این منظور در نظر گرفته شده است. روش پیشنهادی در این مقاله با روش‌های مشابه در مقالات دیگر از پیچیدگی کمتری برخوردار است و در عین حال توانایی بالایی از جمله ناوابستگی به تعداد ابعاد (تعداد نرون‌ها) مسئله دارد. همچنین در این مطالعه شرایط جدیدی براساس ماتریس اتصالات برای پایداری به‌دست آمد. در انتها با استفاده از نرم افزار سیمولینک (وابسته به متلب) شبیه‌سازی یک مدل شش نرونی (که در هر لایه سه نرون می‌باشد) ارائه شده ‌است. نتایج حاصل از شبیه‌سازی کارایی روش مورد نظر را تایید کرد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Investigation stability of a delayed Bidirectional Associative Memory (BAM) neural network

نویسندگان [English]

  • Zahra Mohammadzadeh 1
  • Asadollah Mahmoudzadeh Vaziri 2
  • Asad Azemi 3
  • Omid Rabieimotlagh 4
1 PhD student in Mathematics, Department of Mathematical Sciences and Statistics, Birjand University, Iran.
2 Assistant Professor, Department of Mathematical Sciences and Statistics, Birjand University, Iran
3 Professor, Department of Electrical and Computer Engineering, Wisconsin-Platteville University, USA
4 Associate Professor, Department of Mathematical Sciences and Statistics, Birjand University, Iran.
چکیده [English]

In this paper, the stability of a delayed Bidirectional Associative Memory (BAM) neural network consisting of two layers has been investigated. The approach includes linearization of the BAM neural network, obtaining the characteristic equation, analyzing the nature of its roots, and obtaining the condition for the systems' stability. The results show that the neural network is asymptotically stable when the eigenvalues have a negative real part. Next, the effect of delay in creating oscillation in the system was investigated, and the relevant parameter was obtained. Compared to the other published work in this area, an advantage of the proposed approach is its ability to identify the system's stability in a much more straightforward and less complicated method. Finally, a 2-layer neuron network simulation, with three neurons in each layer, using Simulink software (affiliated with MATLAB), is presented. The simulation results confirm the efficiency of the proposed method.

کلیدواژه‌ها [English]

  • Stability
  • Characteristic function
  • Linearization
  • Bidirectional Associative Memory (BAM) Neural Network
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