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Chaos and strange attractors in coupled oscillators with energy-preserving nonlinearity

Adi-Kusumo F.a,b, Tuwankotta J.M.a, Setya-Budhi W.a

a Analysis and Geometry Group, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Indonesia
b Jurusan Matematika, FMIPA, Universitas Gadjah Mada, 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]We present an analysis for a particular singularly perturbed conservative system. This system comes from the normal form of two coupled oscillator systems with widely-separated frequencies and energy-preserving nonlinearity. The analysis is done in this paper for a degenerate case of such a system, while the generic one has been treated in the literature. To understand the relation with the strong resonance case, we have computed the normal form of the 2:1 resonance, and found that the latter is contained in our system. We present a theorem that gives the existence of a nontrivial equilibrium for a general singularly perturbed conservative system. We detect that the nontrivial equilibrium undergoes two Hopf bifurcations. Furthermore, the periodic solutions created through these Hopf bifurcations undergo a sequence of period doubling bifurcations. This leads to the presence of chaotic dynamics through Shil’nikov bifurcation of a homoclinic orbit. Also, we measure the size of the chaotic attractor which is created in our system. © 2008 IOP Publishing Ltd.[/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][/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/10.1088/1751-8113/41/25/255101[/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]