最新刊期

    卷 65 , 期 5 , 2026

      Research articles

    • Zhu Haojie, Zhao Tongtiegang, Liu Pei, Chen Wenlong
      Vol. 65, Issue 5, Pages: 1-12(2026) DOI: 10.11714/acta.snus.ZR20260027
      摘要:Understanding historical and future water resources dynamics is essential for sustainable basin management. Using the Budyko equation and CMIP6 multi-model data, a total differential approach was applied to quantify the contributions of precipitation and potential evapotranspiration to water resource dynamics across China’s major river basins. Historical observations indicate that water resources declined in over 40% of the country, with an 80% confidence interval of -4.13 to -2.01 mm/a. Under the SSP126, SSP370, and SSP585 scenarios, water resources show overall increases but with significant spatiotemporal variability and uncertainty. For river basins in Southwest China, the projected variation ranges are -11.16% to 20.49%, -14.70% to 28.62%, and -10.89% to 46.43%, respectively. Attribution analysis across nine representative basins reveals that reduced precipitation and increased potential evapotranspiration jointly drive water resource declines in more than 60% of years, with dominant drivers varying by basin and scenario. The relative contribution of decreasing precipitation gradually increases with rising aridity index. Reduced precipitation remains the dominant factor in arid regions, with contribution on rates of 0.93 for the historical period and 0.65, 0.60, and 0.60 for the three future emission scenarios, respectively. This study provides a scientific basis for the long-term optimal allocation of water resources in China’s major river basins.  
      关键词:water resources;Budyko equation;evapotranspiration;total differential equation;climate change   
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    • Shen Chong, Liu Yiming, Chen Xi, Chen Xiaoyang, Fan Qi, Wang Xuemei, Wu Xiaoxuan, Lan Jing, Wu Jie
      Vol. 65, Issue 5, Pages: 13-25(2026) DOI: 10.11714/acta.snus.ZR20260088
      摘要:The default urban morphology parameters in the WRF (weather research and forecasting) model are spatially homogenized and cannot adequately characterize the spatial heterogeneity of real urban underlying surfaces. To investigate the impacts of localized urban morphology parameters on thermodynamic environment simulations using different urban canopy schemes in the WRF model, this study takes the megacity of Guangzhou as a case study and conducts sensitivity experiments. The simulation performances of the single-layer urban canopy (UCM) and the multi-layer building effect parameterization (BEP) schemes for near-surface meteorological elements under the default and localized parameters settings are compared. The results show that: 1) The optimization effects of the localized urban morphology parameters differ significantly between the two schemes. The most notable improvements are found in 2 m temperature for the UCM scheme and in 10 m wind speed for the BEP scheme, with bias reduction rates reaching 90.1% and 49.8%, respectively. More than 71% of stations exhibit improved performance in 2 m temperature simulations, and over 93% show enhanced capability in 10 m wind speed simulations. 2) The localized urban morphology parameters lead to increases in simulated surface skin temperature in both schemes, with a more pronounced rise in the central urban area. Specifically, the BEP scheme demonstrates a greater temperature rise due to narrowed street canyons and enhanced heat trapping. The impact of these parameters on surface skin temperature is greater than that on 2 m temperature. 3) Due to increased surface roughness induced by larger standard deviations of building height, the 10 m wind speeds in both schemes decrease by more than 0.8 m/s. These parameters cause the planetary boundary layer height to increase by 60-90 m in the UCM scheme, while it decreases by 10-30 m in the BEP scheme. These differences are closely related to changes in 2 m temperature and vertical turbulent momentum exchange. This study clarifies the response characteristics of different urban canopy schemes to urban morphology parameters, refines the localized application of these parameters in the WRF model,and provides technical support for high-resolution urban climate simulations.  
      关键词:urban canopy scheme;urban morphological parameter;thermodynamic environment;WRF model;Guangzhou   
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    • Shi Zhuoxuan, Li Qiding, Xu Weiwei, Peng Jianbing, Luo Song, Lü Jinyu
      Vol. 65, Issue 5, Pages: 26-35(2026) DOI: 10.11714/acta.snus.ZR20260020
      摘要:The H-κ stacking method, commonly used to estimate crustal thickness and velocity ratio from receiver functions, has recently been extended to extract structural parameters of sedimentary layers. However, in ancient, high-velocity sedimentary strata, the H-κ spectrum is often contaminated by a continuous high-amplitude strip near zero depth caused by the direct P-wave. This renders the traditional criterion-selecting parameters based on the global maximum stacking amplitude-invalid, making it difficult to identify the sedimentary basement interface. To address this issue, we propose an optimized H-κ scanning method based on the flood-fill algorithm. The method treats the H-κ spectrum as a two-dimensional energy terrain and analyzes its connectivity structure. It automatically identifies and removes the non-physical high-amplitude region connected to the zero-depth boundary, thereby determining the optimal H-κ parameters within a topologically closed energy basin. This approach requires no additional velocity model or empirical depth threshold and preserves the original physical framework of the H-κ method. Synthetic tests and feild data applications from a short-period dense array on the western margin of the Ordos Block demonstrate that the improved method effectively suppresses interference from the zero-depth spurious peak and accurately identifies sedimentary thickness and velocity ratio.  
      关键词:sedimentary thickness;receiver function;H-κ scanning;flood-fill algorithm;western margin of the Ordos Block   
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    • Huang Hongwei, Guo Feng, Li Yulong, Yang Daiquan, Gao Feng, Pang Rui, Li Lin, Li Shiying, Fang Junrong, Li Guanhua
      Vol. 65, Issue 5, Pages: 36-47(2026) DOI: 10.11714/acta.snus.ZR20250232
      摘要:Coastal environmental changes resulting from global climate change has significant implications for regional development. Hailing Bay, located in the northern South China Sea, preserves a continuous Holocene sedimentary archive, making it ideal for reconstructing paleoenvironmental evolution. This study examined the offshore HLZZ08 core and established a chronological framework using radiocarbon (14C) and optically stimulated luminescence dating. Grain‑size parameters were used to build sedimentary sequences. End‑member modeling, grain‑size standard deviation analysis, and principal component analysis were applied to explore the relationship between grain‑size variability and regional environmental change. The sediment grain size distributions in core HLZZ08 are primarily unimodal to bimodal, indicating multi‑stage shifts in depositional dynamics. The fine‑grained components reflect variations in summer monsoon intensity and fluvial discharge, whereas the coarse‑grained fractions correspond to stronger fluvial and marine hydrodynamic conditions during lower sea‑level periods. Grain‑size variations reveal a strengthening summer monsoon in the early Holocene, followed by a progressive weakening in the mid‑Holocene, with depositional dynamics primarily controlled by monsoon intensity and sea‑level fluctuations. Over the past 2 000 years, the sedimentary evolution shifted from being monsoon‑dominated to sea‑level‑controlled. During this period, fine particles remained sensitive to summer monsoon variability, while coarse particles primarily tracked sea‑level changes. Concurrently, grain‑size fluctuations over the last millennium have also shown a degree of synchrony with regional indicators of human activity. These findings provide new insights into Holocene environment-human interactions in Hailing Bay and advance paleoenvironmental research in the northern South China Sea.  
      关键词:Holocene;grain size analysis;Paleoenvironment;Hailing Bay;South China Sea   
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    • Li Yue, Luo Lijuan, Luan Tiangang
      Vol. 65, Issue 5, Pages: 48-57(2026) DOI: 10.11714/acta.snus.ZR20260052
      摘要:Polycyclic aromatic hydrocarbons (PAHs) are a class of persistent organic pollutants widely distributed in the air, water and soil. They are teratogenic, carcinogenic and mutagenic, posing a serious threat to the safety of aquatic ecosystems. As primary producers in aquatic ecosystems, algal photosynthetic systems are sensitive targets of PAHs toxicity, but the mechanisms of PAHs-induced damage and transcriptional regulation on algal photosynthetic systems remain unclear. In this study, the model freshwater green alga Raphidocelis subcapitata was used as the research object, combining chlorophyll fluorescence imaging technology and transcriptomic analysis to explore the effects of PAHs on the algal photosynthetic system and its regulatory mechanism. The results showed that the inhibitory effect of benzo[a]pyrene on the maximum photochemical efficiency of R. subcapitata was generally weaker than that of phenanthrene (PHE) and pyrene (PYR). The electron transport rate of algae in the PHE and PYR treatment groups decreased to 43% and 49% of the control group, respectively, while PAHs exposure had little effect on the non-photochemical quenching coefficient of algae. The expression of five key genes in the algal photosynthetic system (cabII-1, LHCA4, LHCA5, PsbP and PsaN) was time-dependent, showing a significant upward trend on days 3 to 5 of exposure and decreasing on day 7. With the extension of exposure time, the transcriptional regulation mechanism of the algal photosynthetic system gradually became imbalanced, eventually leading to continuous damage to photosynthetic function. This study clarified the damage mechanism and transcriptional regulation characteristics of PAHs on the algal photosynthetic system at the physiological and molecular levels, providing a theoretical reference for the ecotoxicological study of PAHs and the assessment of aquatic ecological risks.  
      关键词:polycyclic aromatic hydrocarbons;Raphidocelis subcapitata;transcriptomics;photosynthesis   
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    • Wang Mengqi, Li Xujie, Zhang Xuejiao, He Chunmei, Zhong Zhiming, Mo Gangyi, Zou Yanli, Zhao Wanyi, Liao Wenbo, Fan Qiang
      Vol. 65, Issue 5, Pages: 58-69(2026) DOI: 10.11714/acta.snus.ZR20260030
      摘要:Camellia granthamiana is a plant species endemic to China with a small population, and is listed as a key protected species in Guangdong Province. Studies on its community structure are of great significance for its conservation and management. In this research, plot surveys were conducted in five C. granthamiana communities distributed in Guangdong Province, and the survival status of the species was analyzed from three dimensions: Community structure, species diversity, and phylogenetic structure. The results showed that: (1) Among the five communities, the age structure of C. granthamiana populations was of the growing type. In Baixi of Zijin County (BX-1, BX-2) and Heishiding (HSD-1), C. granthamiana was the dominant species in the lower and middle layers of the arbor layer, with sound population regeneration; whereas in the community of Mount Qiniangshan in Shenzhen (QNS-1, QNS-2), the species had a very small population size and existed mainly as an associated species. (2) QNS-1 had the highest species richness and evenness, with the most stable community structure; by contrast, BX-1 had a high dominance of C. granthamiana but a relatively low species evenness. (3) The deep-level phylogenetic structure of QNS-1 and QNS-2 tended to be clustered, indicating that habitat filtering played a leading role in community assembly. On the other hand, the deep-level phylogenetic structure of BX-1, BX-2 and HSD-1 showed a divergent pattern, suggesting that competitive exclusion was the dominant process in community assembly. For the shallow-level phylogenetic structure, the plots QNS-2, BX-1 and BX-2 exhibited a clustered distribution, which reflected the filtering effect of environmental conditions on the composition of closely related species in the community; while the plots QNS-1 and HSD-1 showed a divergent pattern, indicating that competitive exclusion mainly acted among closely related species. (4) The plot QNS-1 is located in the transition zone between the southern subtropical and northern tropical zones, which had the highest phylogenetic diversity, and the most complex species composition. This study reveals that the endangered status of C. granthamiana is the combined result of its narrow geographic distribution, fragile population regeneration ability, human interference and environmental screening. In summary, this study systematically clarifies the structure and construction mechanisms of the natural communities of C. granthamiana based on the data of community ecology and phylogenetics, providing a theoretical basis for the implementation of in-situ conservation and population restoration.  
      关键词:Camellia granthamiana;community structure;species diversity;phylogenetic diversity   
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    • Liu Ziheng, Zhang Zhilong, Liu Hancheng, Wu Xianzhong, Tang Yanlin
      Vol. 65, Issue 5, Pages: 70-84(2026) DOI: 10.11714/acta.snus.ZR20260081
      摘要:To solve the limitations of traditional adenosine content determination methods, such as complex sample preparation and time-consuming operations, in this study, Fourier transform infrared (FTIR) spectroscopy combined with chemometric methods was employed to establish a rapid detection model for adenosine content in Cordyceps sinensis. A rapid, efficient, and non-destructive quantitative method was proposed based on FTIR spectroscopy integrated with Simpson's integration rule. Spectral data were collected from 77 samples of C. sinensis. Through statistical analysis, 1 365 significant data points were screened from 1 868 original data points, determining five critical wavenumber regions (399.19-833.29, 1 033.36-1 380.46, 1 710.13-1 790.89, 1 870.56-3 020.78, and 3 980.46-3 999.71 cm-1). Four types of spectral characteristic variables — peak area (A), full width at half maximum (FWHM), area-to-height (H) ratio (A/H), and mean absorbance of the spectral band (MBA). A total of 62 samples (80%) were allocated as the training-validation set for 5-fold cross-validation to establish Multiple Linear Regression (MLR) and Partial Least Squares Regression (PLSR) models; the remaining 15 samples (20%) served as an independent test set for model generalization validation. FTIR characteristic analysis revealed that the principal absorption peaks of C. sinensis were located at 3 289.17 cm-1 (O—H stretching), 2 928.53 cm-1 (asymmetric C—H stretching), and 1 652.72 cm-1 (amide I band). Modeling results demonstrated that the A/H ratio feature exhibited optimal performance on the calibration set (MLR: R²=0.941±0.029), but suffered from severe overfitting (ΔR²=0.225); the PLSR-MBA combined model achieved the best cross-validation performance (R²=0.807±0.031, RMSE=0.189±0.005) with minimal overfitting (ΔR²=0.078). Independent test set validation further confirmed the superior predictive accuracy and robustness of the PLSR-MBA model (R²=0.886, RMSE=0.107), significantly outperforming the MLR-A/H model (R²=0.845, RMSE=0.169). The PLSR-MBA combined model achieves an optimal balance among fitting accuracy, generalization capability, and overfitting resistance, and is recommended as the preferred method for rapid quantitative analysis of adenosine content in C. sinensis. This study provides theoretical basis and practical guidance for feature extraction and modeling strategy selection in spectral quantitative analysis of traditional Chinese medicines.  
      关键词:chemometric methods;Cordyceps sinensis;adenosine;infrared spectroscopy;Simpson's rule;partial least squares regression;multiple linear regression   
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    • Huang Nengneng, Liu Lujie, Zhou Yehao, Fan Yiping, Xiao Leyuan, Wen Zhiming, Liu Zhijun, Chen Heru
      Vol. 65, Issue 5, Pages: 85-98(2026) DOI: 10.11714/acta.snus.ZR20250267
      摘要:Twenty-five hybrids as andrographolide(AG) molecular structural form similaritity analogues AG-Sn(n=1-25) were designed and synthesized,where the flexible trans-decahydronaphthalene with exocyclic double bond moiety of AG was replaced by rigid naphthalene ring,and α,β-unsaturated-γ-butyrolactone was replaced by flexible linear α,β-unsaturated amide. The total yield of these 11-step reactions was 29%-35%. All hybrids are reported here for the first time. The experimental results revealed that the α,β-unsaturated amide scaffold significantly influences the anticancer activity of these hybrids. Just the same as AG,hybrids with rigidity,high steric hindrance,and high-tension substituents on the nitrogen atom of amide bond including AG-S2,AG-S4,AG-S5,AG-S6,AG-S7,and AG-S16 were demonstrated with good antitumor activity against rat glioma cells(C6),human liver cancer cells(HepG-2),human colon adenocarcinoma cells(Caco2),human malignant melanoma cells(A-375),and human breast cancer cells(MDA-MB-231),exhibiting broad-spectrum anticancer activity. Among them,compound AG-S2 exhibits the most prominent anticancer activity against C6,with an IC50 value of(0.9±0.2) μmol/L,which is 10-fold more active than that of AG. All these six compounds were indicated with higher inhibitory activity on HepG-2 cells than that of AG. The structure-activity relationship(SAR) study reveals that hybrids with α,β-unsaturated amide bonds with double substitutions on nitrogen atom generally exhibit better anticancer activity. All the above results indicate that molecular structural form similarity is an effective way to search for new drug candidates.  
      关键词:molecular structural form similarity;andrographolide;antitumor;drug design;drug synthesis   
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    • Yuan Zhoulü, He Zhaocheng, Xie Chuanzhi
      Vol. 65, Issue 5, Pages: 99-108(2026) DOI: 10.11714/acta.snus.ZR20260066
      摘要:In practical intelligent transportation systems,failures of IoT may lead to data interruption, underscoring the importance of trajectory data generation algorithms. Existing trajectory generation methods can be categorized into two types, both of which exhibit limitations. Physics-based algorithms are unable to adapt to dynamically changing traffic scenarios, whereas data-driven methods tend to overlook interactions among vehicles. To address complex scenarios such as intersections, this paper proposes a trajectory generation method based on a conditional diffusion model. The proposed method introduces a motif matrix to quantify the influence of surrounding vehicles on the target vehicle,and employs a graph attention mechanism to accurately identify key neighboring vehicle information, and the conditional information is incorporated into the reverse denoising process of the diffusion model to generate vehicle trajectories. Experiments conducted on the nuScenes dataset and a self-collected trajectory dataset demonstrate that the proposed method outperforms existing mainstream models across multiple accuracy evaluation metrics and is more consistent with kinematic principles.  
      关键词:intelligent transportation;vehicle trajectory generation;conditional diffusion model   
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    • Lei Yilin, Li Yudong, Chen Cheng, Hu Tianjiang
      Vol. 65, Issue 5, Pages: 109-117(2026) DOI: 10.11714/acta.snus.ZR20260065
      摘要:Existing studies mostly focus on sensing external environments and targets by drones, with limited attention to onboard perception of active external detection. To solve this problem, this paper proposes a photosensitive sensing anti-detection flight method for drone swarms. First, we develop a compact photosensitive sensor unit that measures ambient directional illumination at each point in space around the drone. Based on the above, we devise an anti-detection evasion strategy by combining online observation and history weighting, and couple it with a risk propagation anti-detection model to enable local evasion knowledge sharing and coordination within the swarm. In addition, an onboard photosensitive experimental platform is constructed for local directional light-intensity observation. Experimental results show that, in the single-drone scenario, compared with no avoidance strategy, the proposed approach reduces the mean exposure time inside the threat area by 27.90%, with a maximum heading change of 46.80° during avoidance. For the swarm-cooperative case, our approach can reduce the average swarm exposure time by 26.62% compared with the strategy without anti-detection, and by 9.39% compared with the traditional velocity averaging strategy. The results provide a useful reference platform, experimental data, and theoretical support for coordinated anti-detection flight in drone swarms.  
      关键词:drone swarms;anti-detection;photosensitive sensing;swarm traversal;detection area   
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    • AGV autonomous intelligent navigation algorithm based on improved DDPG

      Chen Yongcan, Huang Xiao, Liang Haicheng, Tang Chengpei
      Vol. 65, Issue 5, Pages: 118-128(2026) DOI: 10.11714/acta.snus.ZR20260118
      摘要:An autonomous intelligent navigation algorithm for automatic guided vehicles(AGV) based on an improved deep deterministic policy gradient(DDPG) is proposed.First,an adaptive exploration strategy based on environmental risk is introduced,which includes predicting the trajectories of dynamic obstacles. Next, a multi-objective weighted reward function is designed to guide the AGV to reach its destination as quickly as possible while avoiding obstacles and staying within boundaries.Then,experiences are extracted using a dual-factor approach based on risk coefficients and experience freshness,which shortens the training cycle and improves training quality. Finally,action rehearsal during runtime further reduces the risk of collisions and boundary violations. To validate the algorithm's performance,simulation experiments were conducted under different numbers,sizes,and speeds of obstacles.The results showed that the AGV navigation algorithm based on the improved DDPG achieved an average success rate of 94.8%, an average timeout rate below 3%,and an average collision rate below 2.3%. Moreover,both the training cycles and navigation time were shorter than those of comparison algorithms, showing clear advantages.  
      关键词:deep reinforcement learning;DDPG;AGV;intelligent navigation   
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    • Measurement and allocation methods for carbon emissions from vehicles

      Yan Shengyu, Hao Shijie, Wang Shangjun, Zhao Chenglong, Zhao Lingyu
      Vol. 65, Issue 5, Pages: 129-136(2026) DOI: 10.11714/acta.snus.ZR20260096
      摘要:A top-down approach for measuring vehicle carbon emissions and allocating them to the road network was proposed. Utilizing the statistical energy consumption data of vehicles from public transit enterprises and carbon emission factors, calculation methods for battery electric vehicles (BEVs), plug-in hybrid electric vehicles(PHEVs), and traditional fuel vehicles were studied. Relying on the longitude, latitude, and vehicle speed parameters from high-frequency GPS data, 15 km/h was set as the threshold for determining the driving state. Based on the driving coefficient and the auxiliary equipment time penalty coefficient, the relative carbon emission penalty weight for each trajectory point was determined. Furthermore, the spatial congestion penalty coefficient was utilized to correct road segment attributes, and an improved network kernel density function was applied to assign values to the road segments of the transit network. By calculating the normalized weight of each road segment, the total carbon emissions of vehicles were allocated to the transit network according to the weights, thereby determining the carbon emission intensity of each road segment. The results indicate that the proposed measurement and network allocation method for public transit vehicle carbon emissions is feasible, as verified by a case study. The total carbon emissions of public transit vehicles in the example city in 2024 are 204 300 tons. The carbon emissions per 100 km of medium-sized BEVs and large BEVs account for only 59.10% and 65.35% of those of compressed natural gas(CNG) vehicles of the same length, respectively. When the vehicle speed is lower than 15 km/h, the relative carbon emission penalty weight exhibits a non-linear heavy-tailed distribution characteristic. High carbon emission areas are significantly concentrated in congested road segments characterized by heavy traffic volume, dense transit stops, high network density, and frequent traffic lights. The research results will support the optimization of green and low-carbon public transit networks and the targeted governance of local high-carbon-emission road segments.  
      关键词:urban public transportation vehicles;top-down approach;carbon emission factor;kernel density estimation   
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    • Spectra and norms of algebraic combinations of projection pairs

      Zhu Tong, Song Xianhua
      Vol. 65, Issue 5, Pages: 137-146(2026) DOI: 10.11714/acta.snus.ZR20260012
      摘要:This paper first investigates the spectra of the product PQ, Jordan product PQ+QP, triple Jordan product PQP, quasi-product P+Q-PQ and Lie product PQ-QP for pairs of projections P,Q on Hilbert space H. Secondly, it investigates the spectra and norms of the linear combination αP+βQα,β∈C\{0} of projection pairs. Meanwhile, the relationships between the norms of the sum, difference, product, Jordan product and Lie product of non-zero projection pairs are also derived.  
      关键词:pair of projection;generic pair of projection;spectrum of operator;norm   
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    • Xu Ling, Xie Jingyi
      Vol. 65, Issue 5, Pages: 147-158(2026) DOI: 10.11714/acta.snus.ZR20260022
      摘要:The existence and uniqueness of solutions,as well as the existence of global attractors and strong global attractors are investigated for a class of Kirchhoff-type beam equations with degenerate nonlocal strong damping. Firstly, we establish the existence and uniqueness of weak solutions by employing the Faedo-Galerkin approximation along with interpolation inequalities. Secondly, by constructing a bounded absorbing set,we establish the asymptotic compactness of the solution semigroup, and thereby obtain the existence of a global attractor in the topological space ℋ. Finally, we apply the norm-to-weak continuous semigroup theory and condition (C), to show that the system also has a global attractor in the stronger topological space ℋ1 /q.  
      关键词:beam equation;Kirchhoff-type;degenerate nonlocal strong damping;existence and uniqueness of weak solutions;global attractor   
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    • Turing-Hopf bifurcation of a minimal sediment model with diffusion

      Wang Jingjing
      Vol. 65, Issue 5, Pages: 159-167(2026) DOI: 10.11714/acta.snus.ZR20260006
      摘要:A minimal sediment model with diffusion is proposed. Firstly, the existence of Turing-Hopf bifurcation for the model is investigated; Secondly, the normal form of model at the Turing-Hopf bifurcation point is derived; Finally, the dynamics of model are analyzed by means of numerical results. The research indicates that near the Turing-Hopf bifurcation point, the model exhibits rich spatiotemporal dynamics, including the spatially homogeneous periodic solutions, spatially inhomogeneous periodic solutions and spatially inhomogeneous steady-state solutions.  
      关键词:minimal sediment model;Turing-Hopf bifurcation;normal form;spatiotemporal dynamics   
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    • Zhang Yali
      Vol. 65, Issue 5, Pages: 168-176(2026) DOI: 10.11714/acta.snus.ZR20260036
      摘要:The existence of solutions for a class of superlinear second-order discrete Neumann boundary value problems of the form-Δ2ut-1=u+tp+ft,   t∈1,TZ,Δu0=ΔuT=0,whereis an integer, p>1, and f satisfies the condition ∑t=1T f(t)<0, is investigated. Based on the topological degree theory, we show that the problem possesses at least one solution. Additionally, we extend our analysis to systems of second-order discrete equations with similar nonlinearities.  
      关键词:discrete equations;resonance;superlinearity;topological degree   
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