Complex Dynamics of a Predator-Prey System With Gompertz Growth and Herd Behavior
The complex dynamics of a predator-prey system in discrete time are studied. In this system, we consider the prey’s Gompertz growth and the square-root functional response. The existence of fixed points and stability are examined. Using the center manifold and bifurcation theory, we found that the s...
Saved in:
| Published in | International journal of analysis and applications Vol. 21; p. 100 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Etamaths Publishing
01.01.2023
|
| Online Access | Get full text |
| ISSN | 2291-8639 2291-8639 |
| DOI | 10.28924/2291-8639-21-2023-100 |
Cover
Loading…
| Abstract | The complex dynamics of a predator-prey system in discrete time are studied. In this system, we consider the prey’s Gompertz growth and the square-root functional response. The existence of fixed points and stability are examined. Using the center manifold and bifurcation theory, we found that the system undergoes transcritical bifurcation, period-doubling bifurcation, and Neimark-Sacker bifurcation. In addition, numerical examples are presented to illustrate the consistency of the analytical findings. The bifurcation diagrams show that the positive fixed point is stable if the death rate of the predator is greater than a threshold value. Biologically, it means that to prevent the predator population from growing uncontrollably and stability of the positive fixed point, the predator’s death rate should be greater than the threshold value. |
|---|---|
| AbstractList | The complex dynamics of a predator-prey system in discrete time are studied. In this system, we consider the prey’s Gompertz growth and the square-root functional response. The existence of fixed points and stability are examined. Using the center manifold and bifurcation theory, we found that the system undergoes transcritical bifurcation, period-doubling bifurcation, and Neimark-Sacker bifurcation. In addition, numerical examples are presented to illustrate the consistency of the analytical findings. The bifurcation diagrams show that the positive fixed point is stable if the death rate of the predator is greater than a threshold value. Biologically, it means that to prevent the predator population from growing uncontrollably and stability of the positive fixed point, the predator’s death rate should be greater than the threshold value. |
| Author | Ahmed, Rizwan Almatrafi, M. B. |
| Author_xml | – sequence: 1 givenname: Rizwan surname: Ahmed fullname: Ahmed, Rizwan – sequence: 2 givenname: M. B. surname: Almatrafi fullname: Almatrafi, M. B. |
| BookMark | eNqFUNtKAzEUDFLBWvsLkh9YzWW7mwVftGpbKKio-BjO5mJTtpuSDWr9etMqRXzx6cyZOTMH5hj1Wt8ahE4pOWOiYvk5YxXNRMGrjNGMEcYzSsgB6u_53i98hIZdtySEUJ7nrKB99DD2q3VjPvD1poWVUx32FgO-D0ZD9CFLYIMfN100K_zi4gJP0r0J8RNPgn9PO7QaT03Q-Mos4M35cIIOLTSdGf7MAXq-vXkaT7P53WQ2vpxnihdVzJTQXANjoiYjJiBXoESuRzWrBE-UqQipNE0aEVwZysuiroUtLQetKlbkfIBm37naw1Kug1tB2EgPTu4IH14lhOhUY6S21gC1RUnsKE9_QBuq6jpXvKzNyIqUVXxnqeC7Lhi7z6NE7nqW2w7ltkPJqNz2nCSSjBd_jMpFiM63MYBr_rN_Ab4PhTg |
| CitedBy_id | crossref_primary_10_1080_27690911_2024_2420953 crossref_primary_10_1371_journal_pone_0306734 crossref_primary_10_1007_s11082_024_06471_y crossref_primary_10_1016_j_rinp_2023_107284 crossref_primary_10_1016_j_padiff_2024_100932 crossref_primary_10_1016_j_padiff_2024_100783 crossref_primary_10_3934_math_2024976 crossref_primary_10_1007_s11082_023_05958_4 crossref_primary_10_1007_s12346_024_01124_7 crossref_primary_10_1142_S0218127424501712 crossref_primary_10_1142_S0217984925501039 crossref_primary_10_1007_s40435_024_01551_z crossref_primary_10_1209_0295_5075_ad5eb8 crossref_primary_10_1007_s00033_024_02225_8 crossref_primary_10_1038_s41598_024_74323_6 |
| ContentType | Journal Article |
| DBID | AAYXX CITATION DOA |
| DOI | 10.28924/2291-8639-21-2023-100 |
| DatabaseName | CrossRef Directory of Open Access Journals (DOAJ) |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | CrossRef |
| Database_xml | – sequence: 1 dbid: DOA name: Directory of Open Access Journals (DOAJ) url: https://www.doaj.org/ sourceTypes: Open Website |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences |
| EISSN | 2291-8639 |
| EndPage | 100 |
| ExternalDocumentID | oai_doaj_org_article_dffea1f670f54ac8ade1cbb4c37be5f8 10_28924_2291_8639_21_2023_100 |
| GroupedDBID | 5VS AAYXX ADBBV ALMA_UNASSIGNED_HOLDINGS BCNDV CITATION GROUPED_DOAJ KQ8 M~E OK1 RNS |
| ID | FETCH-LOGICAL-c369t-c8d3da228b0528a4cac84d5b2983b05e9009d1052083ce1376bb8f7f3adc92643 |
| IEDL.DBID | DOA |
| ISSN | 2291-8639 |
| IngestDate | Wed Aug 27 01:13:57 EDT 2025 Tue Jul 01 04:26:28 EDT 2025 Thu Apr 24 23:02:05 EDT 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Language | English |
| License | https://creativecommons.org/licenses/by/4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c369t-c8d3da228b0528a4cac84d5b2983b05e9009d1052083ce1376bb8f7f3adc92643 |
| OpenAccessLink | https://doaj.org/article/dffea1f670f54ac8ade1cbb4c37be5f8 |
| PageCount | 1 |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_dffea1f670f54ac8ade1cbb4c37be5f8 crossref_primary_10_28924_2291_8639_21_2023_100 crossref_citationtrail_10_28924_2291_8639_21_2023_100 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2023-01-01 |
| PublicationDateYYYYMMDD | 2023-01-01 |
| PublicationDate_xml | – month: 01 year: 2023 text: 2023-01-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationTitle | International journal of analysis and applications |
| PublicationYear | 2023 |
| Publisher | Etamaths Publishing |
| Publisher_xml | – name: Etamaths Publishing |
| SSID | ssj0001344261 |
| Score | 2.3383884 |
| Snippet | The complex dynamics of a predator-prey system in discrete time are studied. In this system, we consider the prey’s Gompertz growth and the square-root... |
| SourceID | doaj crossref |
| SourceType | Open Website Enrichment Source Index Database |
| StartPage | 100 |
| Title | Complex Dynamics of a Predator-Prey System With Gompertz Growth and Herd Behavior |
| URI | https://doaj.org/article/dffea1f670f54ac8ade1cbb4c37be5f8 |
| Volume | 21 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV3LSgMxFA3SlRvfYn2RhdvQmTymydJXWwRFwWJ3Q54olFamI6hf701mLHXVjbuZYTKEMze554TkXIQuFAfaqZ0mlJmMcJo5IgtriRLaOCoCVS4KxfuHYjTmdxMxWSn1FfeENfbADXA9F4LXeSj6WRBcW6mdz60x3LK-8SKkY76Q81bEVFpdYTxqg-ZIMGgKynuUqhz6wRShOYlFw2EGyv5koxXT_pRdBjtoq6WF-LLpzi7a8LM9tN1SRNwOwMU-eorjd-o_8U1TSX6B5wFr_Fh5F9UzgYsv3LiQ45e3-hUPIy-u6m88BL0N93rm8MhXDrfGiNUBGg9un69HpK2KQCwrVE2sdMxpSqXJBJWaWwCFO2GokgC38ApYk8vj9hbJrM9hAjFGhn5g2lkF9Icdos5sPvNHCBdKK2kcULB-4DTAT5NBWOVzI5IVXBeJX3RK21qGx8oV0xKkQ0K1jKiWEdWS5mVENZogd1Fv2e69Mc1Y2-Iqgr98O5pepwcQCmUbCuW6UDj-j4-coM0UHGmV5RR16urDnwHvqM15CrEfccfT0A |
| linkProvider | Directory of Open Access Journals |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Complex+Dynamics+of+a+Predator-Prey+System+With+Gompertz+Growth+and+Herd+Behavior&rft.jtitle=International+journal+of+analysis+and+applications&rft.au=Ahmed%2C+Rizwan&rft.au=Almatrafi%2C+M.+B.&rft.date=2023-01-01&rft.issn=2291-8639&rft.eissn=2291-8639&rft.volume=21&rft.spage=100&rft_id=info:doi/10.28924%2F2291-8639-21-2023-100&rft.externalDBID=n%2Fa&rft.externalDocID=10_28924_2291_8639_21_2023_100 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2291-8639&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2291-8639&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2291-8639&client=summon |