Purpose – The paper refers to a pair of conjugate systems (master and slave systems) associated by the condition that the evolution of the first is function on its current state and on a future state of the second system, while the evolution of the second system depends on its current state and on a past state of the first system also. The purpose of this paper is to solve particular cases of differential systems of equations which express the behaviour of conjugate systems, in order to see what kind of symmetry or harmony is established in the common evolution of the two systems. Design/methodology/approach – Becoming with the Dubois' definition of conjugate retardation and anticipation variables and his mixed advanced‐retarded differential equations, the paper considers some cases: first case when information about future and past is kept constant, without and with an impulse from the side of the master system, then when information about future and respective past is a variable. Findings – In the case with variable information about future and past, and for a constant shift time, there are found exponential solutions; it has been ascertained that the two trajectories present a symmetry expressed by their proportionality all the time. A definition of symmetry by anticipation and retardation is given. It is also found that a system with uniform linear development cannot be in a symmetry by anticipation and retardation with any other system. Practical implications – In the paper, the practical implications are linked by the relationship between man and his environment and how to consider the data delivered by forecast. Originality/value – The calculus and its results, the notion of symmetry by anticipation and retardation, examples and conclusions, all are original contributions.
Kybernetes – Emerald Publishing
Published: Jan 1, 2009
Keywords: Symmetry; Master system; Anticipation; Retardation; Impulse
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