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A Basic Manual for AUTO-07p in Computing Bifurcation Diagrams of a Predator-Prey Model
Owen L.a, Harjanto E.a
a Analysis and Geometry Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, 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]© 2019, Springer Nature Singapore Pte Ltd.This is a beginner’s manual of AUTO-07p, a continuation and bifurcation software for ordinary differential equation (ODE). AUTO package is available for Windows, Mac OS, or UNIX/Linux platform. The directory auto/07p/demos has many tutorial demos for algebraic system, ODE and partial differential equation. We focus on the continuation of solutions of system of ODE. In this manual, we will learn the main tools in AUTO by doing cusp and pp2 demos step-by-step. In the first example, we will generate one- and two-parameter bifurcation diagrams. The second example is a 2D predator-prey model with the detection of a Hopf bifurcation. We plot some orbits and time series plot. We provide two options for running AUTO, i.e., by using Unix and Python commands.[/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]Algebraic system,AUTO,Bifurcation diagram,Continuation of solutions,Ordinary differential equation (ODE),Predator-prey modeling,Two parameter[/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]AUTO,AUTO-07p,Bifurcation diagram,Dynamical system,Fold bifurcation,Hopf bifurcation[/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]Acknowledgements We would like to express our sincere gratitude to SEAMS School 2018 on Dynamical Systems and Bifurcation Analysis (DySBA) committee for offering us this opportunity. Livia Owen acknowledges the financial support from The Indonesian Education Scholarship Program (LPDP), Ministry of Finance of the Republic of 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/10.1007/978-981-32-9832-3_11[/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]