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2026
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| Online Access: | https://doi.org/10.5281/zenodo.19457267 |
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| _version_ | 1866901972478590976 |
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| author | Ruiz Castillo, Juan Carlos |
| author_facet | Ruiz Castillo, Juan Carlos |
| contents | <p>In this work, we introduce a novel three-dimensional nonlinear dynamical system, hereafter referred to as the Ruiz system, characterized by the interplay of bilinear, quadratic, and trigonometric nonlinearities. </p> <p>We rigorously establish its dissipative nature through explicit computation of the divergence and provide analytical insights into boundedness via Lyapunov-type estimates. The existence of an absorbing region is demonstrated, ensuring long-term confinement of trajectories in phase space.</p> <p>A detailed equilibrium and linear stability analysis is conducted, revealing parameter-dependent transitions in dynamical behavior. Numerical simulations, including bifurcation diagrams and Lyapunov exponent spectra, indicate the emergence of complex dynamics and sensitivity to initial conditions.</p> <p>Although a rigorous proof of the existence of a strange attractor remains open, the system exhibits strong qualitative and quantitative signatures of dissipative chaos, positioning it as a candidate for further analytical and computational investigation within the theory of nonlinear dynamical systems.</p> <p> </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19457267 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Novel Three-Dimensional Dissipative Dynamical System: A Candidate for Complex Attractor Behavior Ruiz Castillo, Juan Carlos <p>In this work, we introduce a novel three-dimensional nonlinear dynamical system, hereafter referred to as the Ruiz system, characterized by the interplay of bilinear, quadratic, and trigonometric nonlinearities. </p> <p>We rigorously establish its dissipative nature through explicit computation of the divergence and provide analytical insights into boundedness via Lyapunov-type estimates. The existence of an absorbing region is demonstrated, ensuring long-term confinement of trajectories in phase space.</p> <p>A detailed equilibrium and linear stability analysis is conducted, revealing parameter-dependent transitions in dynamical behavior. Numerical simulations, including bifurcation diagrams and Lyapunov exponent spectra, indicate the emergence of complex dynamics and sensitivity to initial conditions.</p> <p>Although a rigorous proof of the existence of a strange attractor remains open, the system exhibits strong qualitative and quantitative signatures of dissipative chaos, positioning it as a candidate for further analytical and computational investigation within the theory of nonlinear dynamical systems.</p> <p> </p> |
| title | A Novel Three-Dimensional Dissipative Dynamical System: A Candidate for Complex Attractor Behavior |
| url | https://doi.org/10.5281/zenodo.19457267 |