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Numerous recently introduced chaotic systems exhibit straightforward algebraic representations. In this study, we explore the potential for identifying a global analytic first integral in a generalized 3-dimensional chaotic system (2). Our work involves detailing the model of a new 3-D chaotic system characterized by three Lyapunov exponents-positive, zero, and negative. We depict the phase trajectories, illustrate bifurcation patterns, and visualize Lyapunov exponent graphs. The investigation encompasses both local and global analytic first integrals for the system, providing results on the existence and non-existence of these integrals for different parameter values. Our findings reveal that the system lacks a global first integral, and the presence or absence of analytic first integrals is contingent upon specific parameter values. Additionally, we present a formal series for the system, demonstrating 3D and 2D projections of the system (2) for a given set of initial conditions achieved by selecting alternative values for parameters a, b, c, d, r and l., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Husien, Amen. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Background: MicroRNAs are mentioned as a small non-coding RNAs groups and aberrant miRNA expression was found in hepatocellular carcinoma (HCC) patients. Aim: To evaluate role of plasma MicroRNA-215 as a diagnostic tool in HCC patients. Methods: A prospective study included 195 subjects: healthy controls (group I), cirrhotic patients (group II), and patients with HCC (group III). Clinical examination, radiological and laboratory investigations which included quantification of miR-215 by Real-time qPCR were done for all cases. Results: Spearman’s rank correlation revealed that in HCC group, there was a negative correlation between MiRNA-215 and serum AFP levels and focal size lesion (cm) (rs = -0.72, - 0.94 respectively, p<0.001). Receiver operating characteristics analysis for discrimination between cirrhosis and HCC groups regarding microRNA-215 displayed 78.3% sensitivity, 88.0% specificity at cutoff value of ≤ 1.90. Area under the curve (AUC) was 0.87 (p< 0.001). As regards AFP, it had a sensitivity of 81.7%, a specificity of 66.7 at cutoff value of ≥ 11.50 (ng/mL). Conclusions: Plasma level of miR-215 may be a promising biomarker in HCC diagnosis. Moreover, if miR-215 combined with AFP, it can be used as a diagnostic biomarker, for early detection of HCC.