Anastasiya Kapytina

Solar activity exhibits a dominant decadal timescale embedded in nonlinear multiscale dynamics. We present a minimal autonomous three-mode hybrid model to investigate whether such a timescale can arise from internal nonlinear energy exchange rather than external periodic forcing or direct inheritance of a prescribed modal period. The model couples a slow internal reservoir, a tachocline-associated transfer mode, and a nonlinear magnetic subsystem described by Duffing and Van der Pol–Duffing dynamics. Magnetic-energy release is implemented through a threshold-triggered reset, while a D-index-based structural energy-exchange index characterizes relative magnetic-energy changes. The system develops a persistent bounded hybrid regime with a dominant period of approximately 10 yr. Initial-condition ensembles and variations in the intrinsic modal periods demonstrate that this timescale does not simply track the prescribed 11 yr tachocline period. Parameter studies identify the release depth and magnetic recovery rate as stronger controls, supporting an accumulation–release mechanism of timescale selection. Release events exhibit organized recurrence and significant tachocline-phase preference, with localized event skipping separating spectral and release timescales. Saltation-based Lyapunov analysis reveals no robust positive largest exponent for the baseline regime over the investigated finite-time horizons. These results demonstrate that nonlinear energy exchange combined with threshold-mediated accumulation and release can autonomously generate a robust decadal collective timescale in a reduced nonlinear system.

Kazakhstan is recognized as one of the primary centers of origin of the wild apple Malus sieversii, concentrated mainly in the mountains like Trans-Ile and Zhongar Alatau, as well as parts of the Tarbagatay, Talas Alatau, and Karatau ranges. As the wild progenitor of Malus domestica, M. sieversii harbors a critical genetic diversity essential for apple breeding and conservation efforts. However, its natural populations are increasingly threatened by latent viral infection, which weakens trees, reduces reproduction, and hinders regeneration. In this study, the spread of apple chlorotic leaf spot virus (ACLSV) and apple stem pitting virus (ASPV) was documented in four wild apple populations, with detection rates of 50.2% and 42.2%, respectively. Mixed infections were observed in 28.8% of sampled trees. Apple stem grooving virus (ASGV) was detected exclusively in cultivated orchards, whereas apple mosaic virus (ApMV) and apple necrotic mosaic virus (ApNMV) were not found in either wild forests or cultivated orchards. Using Geographic Information System (GIS) technology, we developed the first spatial distribution maps of these viruses in wild apple forests in the Tian Shan region, revealing site-specific variation and infection rates. These results underscore the importance of monitoring viral infections in wild M. sieversii populations to preserve genetically valuable, virus-free germplasm critical for apple breeding, crop improvement, and sustainable orchard management.