Year: 2025 | Month: June | Volume: 12 | Issue: 6 | Pages: 669-674
DOI: https://doi.org/10.52403/ijrr.20250676
Bifurcation and Dynamics in a 3D System with Quadratic Coupling
Nurcahya Yulian Ashar1, Hafidh Khoerul Fata1
1Department of Mathematics, Faculty of Sciences and Mathematics, Diponegoro University, Semarang, Indonesia.
Corresponding Author: Hafidh Khoerul Fata
ABSTRACT
This research explores the behavior of a three-dimensional autonomous nonlinear system featuring both quadratic and bilinear interaction terms. The system is developed as an extension of the SE8 model proposed by Molaie et al., with modifications that introduce additional nonlinearities through the inclusion of and components in the third equation. Although the system has a single equilibrium point and a relatively simple structure, it displays a wide range of complex dynamical phenomena, such as bifurcations, multistability, and chaotic attractors. To analyze these dynamics, equilibrium points are identified and their local stability is examined using Jacobian matrix linearization, revealing how changes in parameter values can lead to different stability outcomes. A thorough bifurcation study is conducted, focusing especially on the emergence of Hopf bifurcations. The theoretical results are validated through numerical simulations, which include bifurcation diagrams, Lyapunov exponent analysis, and phase portraits that depict the system's transition to chaos and its sensitivity to initial conditions.
Keywords: Nonlinear Dynamical Systems, Quadratic Coupling, Bifurcation Analysis, Chaos Theory, Lyapunov Exponents.
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