In this paper, the dynamics of an autonomous three dimensional system with three nonlinearity quadratic terms is investigated. With the help of stability analysis of equilibrium points, the Lyapunov exponent, and the phase portraits we study the dynamical behavior of the fractional order system. We ﬁnd that system can display double scroll and double-four wing chaotic attractor. The commensurate order has been investigated and we ﬁnd that the necessary condition for chaos to appear is 0.84 <α ≤ 1. For the incommensurate order, we show that the instability measure of the equilibrium points for all the saddle points of index 2 must be non-negative for a system with ﬁve equilibrium points to be chaotic. Numerical simulations and the analog simulations are carried out in Multisim. Keywords Chaos · Fractional order system · Commensurate order · Incommensurate order · Circuit realization 1 Introduction erature is exponentially growing. The Lorenz equation was derived from the Oberbeck–Boussinesq approximation, and The topic of chaos is gaining more attention, and its appli- describes the ﬂuid circulation in a shallow layer of ﬂuid . cation ﬁeld becomes more and more important. Nowadays, That system has only two nonlinear quadratic terms and can we found the
International Journal of Dynamics and Control – Springer Journals
Published: May 29, 2018
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera