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Stability analysis of predator prey model on the case of aerosol-cloud-precipitation interactions
Sulistyowati R.a,b, Kurniadi R.a, Srigutomo W.a
a Physics of Earth and Complex System Research Division, Physics Department, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, 40132, Indonesia
b Physics Department, Faculty of Teacher Training and Science Education, Universitas PGRI Palembang, Palembang, 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]© 2015 AIP Publishing LLC.A preliminary study has been performed on the analysis of the stability of predator-prey models in the case of aerosol-cloud-precipitation interactions which initiated by Koren-Feingold. The model consists of two coupled non- linear differential equations describing the development of a population of cloud drop concentration and cloud depth for precipitation. Stability analysis of the models was conducted to understand the stability behavior of systems interactions. In this paper, the analysis focused on the model without delay. The first step was done by determining the equilibrium point of the model equations which yielded 1 non-trivial equilibrium point and 4 trivial equilibrium point. Nontrivial equilibrium point (0,0) associated with the steady state or the absence of precipitation while the non-trivial equilibrium point shows the oscillation behavior in the formation of precipitation. The next step is linearizing the equation around the equilibrium point and calculating of eigenvalues of Jacobian matrix. Evaluation of the eigen values of characteristic equation determined the type of stability. There are saddle node, star point, unstable node, stable node and center. The results of numerical computations was simulated in the form of phase portrait to support the theoretical calculation. Phase portraits show the characteristic of populations growth of cloud depth and drop cloud. In the next research, this analysis will compared to delay model to determine the effect of time delay on the equilibrium point of the system.[/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][/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]equilibrium points,Jacobian matrix,phase portrait,predator-prey model,stability analysis,type of stability[/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][/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/10.1063/1.4930703[/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]