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## STABILITY AND HOPF BIFURCATION ANALYSIS OF A MATHEMATICAL MODEL IN TUMOR ANGIOGENESIS

#### Serdal Pamuk [1] , İrem ÇAY [2]

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This work has been presented at the ”International Conference on Mathematics and Engineering, 10-12 May, 2017, Istanbul, Turkey”. In this paper we introduce a stability and Hopf bifurcation analysis of a reaction diﬀusion system which models the interaction between endothelial cells and the inhibitor. Then, we investigate the stability of the positive equilibrium solutions under some conditions. We also show the existence of a Hopf bifurcation and provide some figures to show that the equilibrium solutions are indeed asymptotically stable.

Equilibrium solution, Hopf bifurcation
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Konular Mühendislik Araştırma Makalesi Yazar: Serdal PamukÜlke: Turkey Yazar: İrem ÇAYÜlke: Turkey
 Bibtex @araştırma makalesi { aubtda323014, journal = {ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY A - Applied Sciences and Engineering}, issn = {1302-3160}, eissn = {2146-0205}, address = {Eskişehir Teknik Üniversitesi}, year = {2018}, volume = {19}, pages = {50 - 57}, doi = {10.18038/aubtda.323014}, title = {STABILITY AND HOPF BIFURCATION ANALYSIS OF A MATHEMATICAL MODEL IN TUMOR ANGIOGENESIS}, key = {cite}, author = {Pamuk, Serdal and ÇAY, İrem} } APA Pamuk, S , ÇAY, İ . (2018). STABILITY AND HOPF BIFURCATION ANALYSIS OF A MATHEMATICAL MODEL IN TUMOR ANGIOGENESIS. ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY A - Applied Sciences and Engineering, 19 (1), 50-57. DOI: 10.18038/aubtda.323014 MLA Pamuk, S , ÇAY, İ . "STABILITY AND HOPF BIFURCATION ANALYSIS OF A MATHEMATICAL MODEL IN TUMOR ANGIOGENESIS". ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY A - Applied Sciences and Engineering 19 (2018): 50-57 Chicago Pamuk, S , ÇAY, İ . "STABILITY AND HOPF BIFURCATION ANALYSIS OF A MATHEMATICAL MODEL IN TUMOR ANGIOGENESIS". ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY A - Applied Sciences and Engineering 19 (2018): 50-57 RIS TY - JOUR T1 - STABILITY AND HOPF BIFURCATION ANALYSIS OF A MATHEMATICAL MODEL IN TUMOR ANGIOGENESIS AU - Serdal Pamuk , İrem ÇAY Y1 - 2018 PY - 2018 N1 - doi: 10.18038/aubtda.323014 DO - 10.18038/aubtda.323014 T2 - ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY A - Applied Sciences and Engineering JF - Journal JO - JOR SP - 50 EP - 57 VL - 19 IS - 1 SN - 1302-3160-2146-0205 M3 - doi: 10.18038/aubtda.323014 UR - http://dx.doi.org/10.18038/aubtda.323014 Y2 - 2017 ER - EndNote %0 Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi A - Uygulamalı Bilimler ve Mühendislik STABILITY AND HOPF BIFURCATION ANALYSIS OF A MATHEMATICAL MODEL IN TUMOR ANGIOGENESIS %A Serdal Pamuk , İrem ÇAY %T STABILITY AND HOPF BIFURCATION ANALYSIS OF A MATHEMATICAL MODEL IN TUMOR ANGIOGENESIS %D 2018 %J ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY A - Applied Sciences and Engineering %P 1302-3160-2146-0205 %V 19 %N 1 %R doi: 10.18038/aubtda.323014 %U 10.18038/aubtda.323014 ISNAD Pamuk, Serdal , ÇAY, İrem . "STABILITY AND HOPF BIFURCATION ANALYSIS OF A MATHEMATICAL MODEL IN TUMOR ANGIOGENESIS". ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY A - Applied Sciences and Engineering 19 / 1 (Mart 2018): 50-57. http://dx.doi.org/10.18038/aubtda.323014