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On slow–fast dynamics in a classical predator–prey system

Owen L.a, Tuwankotta J.M.a

a Analysis and Geometry Group, Institut Teknologi Bandung, Indonesia

[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]© 2020We study a classical predator–prey system with the assumption that the birth rate of the prey is small in comparison with the death rate of the predator. As a consequence, some solutions of the system might have a slow–fast structure. Using singular perturbation technique and various scalings, we construct an approximation for the solution. Although the explicit formula for the solution is available, the approximation we have constructed describes the time behavior more explicitly. Furthermore, we indicate a domain near an equilibrium where slow–fast dynamics is absent.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Birth rates,Death rates,Explicit formula,Fast dynamics,Scalings,Singular perturbation technique,Time behavior[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Dynamical system,Predator–prey,Singular perturbation,slow–fast dynamics[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text][{‘$’: “Livia Owen acknowledges the financial support from The Indonesian Education Scholarship Program (LPDP), Ministry of Finance of the Republic of Indonesia. J.M. Tuwankotta’s research is supported by research grant Riset ITB 2020, Institut Teknologi Bandung, Indonesia.”}, {‘$’: ‘Livia Owen acknowledges the financial support from The Indonesian Education Scholarship Program (LPDP), Ministry of Finance of the Republic of Indonesia . J.M. Tuwankotta’s research is supported by research grant Riset ITB 2020 , Institut Teknologi Bandung, Indonesia .’}][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text]https://doi.org/10.1016/j.matcom.2020.05.003[/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]