Analyzing the variation in the correlation between the maximum amplitude [Rmax\documentclass[12pt]{minimal}
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\begin{document}$R_{\mathrm{max}}$\end{document}] of the solar cycle and the hemispheric sunspot number [RH\documentclass[12pt]{minimal}
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\begin{document}$R_{\mathrm{H}}$\end{document}], since the previous declining phase, is helpful in understanding the temporal evolution of the cycle and the possible different mechanisms at work in the two hemispheres. The correlation coefficient [r\documentclass[12pt]{minimal}
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\begin{document}$r$\end{document}] between Rmax\documentclass[12pt]{minimal}
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\begin{document}$R_{\mathrm{max}}$\end{document} and the smoothed monthly mean RH\documentclass[12pt]{minimal}
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\begin{document}$R_{\mathrm{H}}$\end{document} as a function of m=−50,−49,…,50\documentclass[12pt]{minimal}
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\begin{document}$m=-\,50,-\,49,\,\ldots ,\,50$\end{document} months from the solar minimum [Rmin\documentclass[12pt]{minimal}
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\begin{document}$R_{\mathrm{min}}$\end{document}] is studied, and it is found that r\documentclass[12pt]{minimal}
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\begin{document}$r$\end{document} is maximum about three years before Rmin\documentclass[12pt]{minimal}
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\begin{document}$R_{\mathrm{min}}$\end{document} at the declining phase, falls to a minimum value around Rmin\documentclass[12pt]{minimal}
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\begin{document}$R_{\mathrm{min}}$\end{document}, and increases with m\documentclass[12pt]{minimal}
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\begin{document}$m$\end{document} during the rising phase in both hemispheres. Based on the highest correlations at the declining phase, the maximum amplitudes of Cycle 25 in the northern [NH] and southern hemisphere [SH] are predicted to be Rmax,N(25)=85.6±21.9\documentclass[12pt]{minimal}
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\begin{document}$R_{\mathrm{max,N}}(25)=85.6\pm 21.9$\end{document} and Rmax,S(25)=74.4±17.9\documentclass[12pt]{minimal}
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\begin{document}$R_{\mathrm{max,S}}(25)=74.4\pm 17.9$\end{document}, respectively. Using data at the rising phase, Rmax,N(25)=84.0±26.7\documentclass[12pt]{minimal}
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\begin{document}$R_{\mathrm{max,N}}(25)=84.0\pm 26.7$\end{document} and Rmax,S(25)=88.3±16.8\documentclass[12pt]{minimal}
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\begin{document}$R_{\mathrm{max,S}}(25)=88.3\pm 16.8$\end{document}. The average values are R‾max,N(25)=84.8±24.3\documentclass[12pt]{minimal}
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\begin{document}$\overline{R}_{\mathrm{max,N}}(25)= 84.8\pm 24.3$\end{document} and R‾max,S(25)=81.4±17.4\documentclass[12pt]{minimal}
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\begin{document}$\overline{R}_{\mathrm{max,S}}(25)=81.4\pm 17.4$\end{document}. According to the weak correlation between the rise time and Rmax\documentclass[12pt]{minimal}
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\begin{document}$R_{\mathrm{max}}$\end{document}, the peak times of Cycle 25 in the NH and SH are predicted to be November 2023 ±10\documentclass[12pt]{minimal}
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\begin{document}$\pm 10$\end{document} months and July 2024 ±10\documentclass[12pt]{minimal}
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\begin{document}$\pm 10$\end{document} months, respectively. Employing the strong correlation between the amplitude of the total sunspot number [Rmax,T\documentclass[12pt]{minimal}
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\begin{document}$R_{\mathrm{max,T}}$\end{document}] and those of RH\documentclass[12pt]{minimal}
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\begin{document}$R_{\mathrm{H}}$\end{document} in both hemispheres (r=0.99\documentclass[12pt]{minimal}
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\begin{document}$r=0.99$\end{document}), the amplitude of Cycle 25 is predicted to be Rmax,T(25)=139.7±28.7\documentclass[12pt]{minimal}
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\begin{document}$R_{\mathrm{max,T}}(25)=139.7\pm 28.7$\end{document} and 152.3±31.5\documentclass[12pt]{minimal}
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\begin{document}$152.3\pm 31.5$\end{document} using data at the declining and rising phases, respectively, with an average value of 146.0±30.1\documentclass[12pt]{minimal}
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\begin{document}$146.0\pm 30.1$\end{document}.
