Unbounded and blow-up solutions for a delay logistic equation with positive feedback
We study bounded, unbounded and blow-up solutions of a delay logistic equation without assuming the dominance of the instantaneous feedback. It is shown that there can exist an exponential (thus unbounded) solution for the nonlinear problem, and in this case the positive equilibrium is always unstab...
| Main Authors: | , , |
|---|---|
| Format: | Journal article |
| Published: |
American Institute of Mathematical Sciences
2018
|
| _version_ | 1826271608317149184 |
|---|---|
| author | Győri, I Nakata, Y Röst, G |
| author_facet | Győri, I Nakata, Y Röst, G |
| author_sort | Győri, I |
| collection | OXFORD |
| description | We study bounded, unbounded and blow-up solutions of a delay logistic equation without assuming the dominance of the instantaneous feedback. It is shown that there can exist an exponential (thus unbounded) solution for the nonlinear problem, and in this case the positive equilibrium is always unstable. We obtain a necessary and sufficient condition for the existence of blow-up solutions, and characterize a wide class of such solutions. There is a parameter set such that the non-trivial equilibrium is locally stable but not globally stable due to the co-existence with blow-up solutions. |
| first_indexed | 2024-03-06T21:59:20Z |
| format | Journal article |
| id | oxford-uuid:4e0e3064-55e4-41b8-90a2-1ec1c720e733 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:59:20Z |
| publishDate | 2018 |
| publisher | American Institute of Mathematical Sciences |
| record_format | dspace |
| spelling | oxford-uuid:4e0e3064-55e4-41b8-90a2-1ec1c720e7332022-03-26T15:58:56ZUnbounded and blow-up solutions for a delay logistic equation with positive feedbackJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:4e0e3064-55e4-41b8-90a2-1ec1c720e733Symplectic Elements at OxfordAmerican Institute of Mathematical Sciences2018Győri, INakata, YRöst, GWe study bounded, unbounded and blow-up solutions of a delay logistic equation without assuming the dominance of the instantaneous feedback. It is shown that there can exist an exponential (thus unbounded) solution for the nonlinear problem, and in this case the positive equilibrium is always unstable. We obtain a necessary and sufficient condition for the existence of blow-up solutions, and characterize a wide class of such solutions. There is a parameter set such that the non-trivial equilibrium is locally stable but not globally stable due to the co-existence with blow-up solutions. |
| spellingShingle | Győri, I Nakata, Y Röst, G Unbounded and blow-up solutions for a delay logistic equation with positive feedback |
| title | Unbounded and blow-up solutions for a delay logistic equation with positive feedback |
| title_full | Unbounded and blow-up solutions for a delay logistic equation with positive feedback |
| title_fullStr | Unbounded and blow-up solutions for a delay logistic equation with positive feedback |
| title_full_unstemmed | Unbounded and blow-up solutions for a delay logistic equation with positive feedback |
| title_short | Unbounded and blow-up solutions for a delay logistic equation with positive feedback |
| title_sort | unbounded and blow up solutions for a delay logistic equation with positive feedback |
| work_keys_str_mv | AT gyorii unboundedandblowupsolutionsforadelaylogisticequationwithpositivefeedback AT nakatay unboundedandblowupsolutionsforadelaylogisticequationwithpositivefeedback AT rostg unboundedandblowupsolutionsforadelaylogisticequationwithpositivefeedback |