Sharp conditions for existence of nontrivial invariant cones of nonnegative initial values of difference equations

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Abstract

It is proved that an arbitrary scalar difference equation has a nontrivial invariant cone in the set of the nonnegative initial values if and only if the associated characteristic equation has a positive root. By using this fact, there is given a construction of the maximal invariant cone in the set of nonnegative initial values via a positive root of the associated characteristic equation. Finally, the present results are compared with some earlier ones which were obtained for delay differential equations in the same direction.

Original languageEnglish
Pages (from-to)89-111
Number of pages23
JournalApplied Mathematics and Computation
Volume36
Issue number2
DOIs
Publication statusPublished - 1990

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Invariant Cone
Characteristic equation
Difference equations
Difference equation
Cones
Non-negative
Roots
Maximal Invariant
Delay Differential Equations
Differential equations
Scalar
If and only if
Arbitrary

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

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abstract = "It is proved that an arbitrary scalar difference equation has a nontrivial invariant cone in the set of the nonnegative initial values if and only if the associated characteristic equation has a positive root. By using this fact, there is given a construction of the maximal invariant cone in the set of nonnegative initial values via a positive root of the associated characteristic equation. Finally, the present results are compared with some earlier ones which were obtained for delay differential equations in the same direction.",
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