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Assuming that the system (1.1) is a system with weak delay, the system (2.7), due to Lemma 1.2, is a system with weak delay again.
Let (1.1) be a system with weak delay and let (2.2) have a simple root.
Let (1.1) be a system with weak delay and (2.2) admit two real distinct roots,.
Let (1.1) be a system with weak delay and let (2.2) have a two-fold root.
Let (1.1) be a system with weak delay, and (2.2) has both roots different from zero.
Theorem 8 Let (1) be a system with weak delay and let (25) have both roots different from zero.
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Assuming that (1) is a system with weak delays, by Lemma 1, system (30) is one with weak delays again.
Lemma 1 If system (1) is a system with weak delays, then its arbitrary linear nonsingular transformation (8) again leads to a system with weak delays (9).
It is assumed that the considered system is one with weak delays.
In the below theorem, we give conditions, in terms of determinants, indicating whether a system is one with weak delays.
If (1) is a system with weak delays, then the corresponding characteristic equation has only two eigenvalues instead of 2 ( m + 1 ) eigenvalues in the case of systems with non-weak delays.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com