KAOTİK ZAMAN SERİSİNİN ANALİZİ ÜZERİNE BİR ARAŞTIRMA

Öz

Bu güne kadar yapılan çalışmalarda, dinamik sistemler doğrusal ve/veya doğrusal olmayan metotlar kullanılarak incelenmişlerdir. Kararlı doğrusal sistemler için kullanılan doğrusal metotlar, doğrusal olmayan analizlerde genellikle başarısız olmakla beraber, yol gösterici olarak kullanılabilmektedir. Dinamik bir sistemi tanımlayan fark denklemlerindeki doğrusal olmayan bir değişkenden dolayı, önceden bilinemeyen dinamikler meydana gelebilir. Kaos teorisi veya doğrusal olmayan analiz metotları bu tür dinamik sistemleri incelemek için kullanılmaktadır. Düzensiz bir durumu ifade eden kaos, “başlangıç koşullarına hassas duyarlılık” olarak tarif edilebilir. Eğer dinamik sistemin fark denklemleri biliniyor ise başlangıç şartlarındaki değişimlerin sistemin dinamiğine etkisi kolaylıkla tespit edilebilir. Deneysel zaman serisi için başlangıç şartının bilinememesi, bu ölçümlerin alındığı sistemlerin analizlerini zorlaştırmaktadır. Bu çalışmada, zaman içinde değişen herhangi bir büyüklüğün belirli aralıklarla ya da sürekli olarak ölçülmesi ile elde edilen zaman serisinin kaotik analizi için kullanılan metotlar açıklanmıştır. Açıklanan metotların çeşitli dinamik sistemlere ait zaman serileri üzerinde uygulamaları yapılmıştır. Özellikle fizyolojik sistemlerden elde edilen zaman serileri üzerinde bu zamana kadar yapılan bazı çalışmalar özetlenmiştir.

Anahtar Kelimeler

• Kaotik analiz, zaman serisi analizi, doğrusal olmayan analiz.

Kaynakça

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