This paper studies the global bifurcation and Hopf bifurcation of one kind of complicated financial system with different parameter combinations. Conditions on which bifurcation happens, and the critical system structure when the system transforms from one kind of topological structure to another are studied as well. The criterion for identifying Hopf bifurcation under different parameter combinations is also given. The chaotic character of this system under quasi-periodic force is finally studied. The bifurcation structure graphs are given when two parameters of the combination are fixed while the other parameter varies. The presence and stability of 2 and 3 dimensional torus bifurcation are studied. All of the Lyapunov exponents of the system with different bifurcation parameters and routes leading the system to chaos with different parameter combinations are studied. It is of important theoretical and practical meaning to probe the intrinsic mechanism of such continuous complicated financial system and to find the macro control policies for such kind of system.
The responses of soil water and winter wheat (Triticum aestivum L.) to changes in precipitation are crucial for stability of wheat yield and soil water conservation in the Chinese Loess Tableland Region (LTR). A 2‐yr (2014‐2016) experiment was conducted in the LTR to investigate soil water dynamics and winter wheat performance under three precipitation levels: Rc (normal), R+ (increased by one‐third of normal), and R− (decreased by one‐third of normal) by a real‐time precipitation allocation system. Soil water storage (SWS) at a depth of 0–3.8 m showed positive (R+) or negative (R−) responses to precipitation. The mean SWS in different soil layers followed an order of R+ > Rc > R−. During the experiment, the 0–3.8 m SWS decreased by 34.5 mm (R+), 183.8 mm (Rc), and 218.9 mm (R−). The shoot biomass and grain yield varied little among three precipitation levels in 2014–2015, but was reduced by 50% in R− compared with Rc in 2015–2016. The R− and Rc treatments had higher water use efficiency (WUE) than R+ in 2014–2015, and Rc was the highest in 2015–2016. The proportions of soil water to water consumption in R+ and Rc increased from 22.5% in 2014–2015 to 42.5% in 2015–2016 on average, and for R− was stable over 2‐yr (average 44.5%). Soil water plays a critical role in winter wheat performance under changes in precipitation, which should guide winter wheat production and soil water management in the future.
Core Ideas
Precipitation changes soil water storage but does not change the regime of soil water changing with time.
Response of winter wheat yield to precipitation change has hysteresis effect.
Supplementary effect of soil water compensates for the negative effect of decreased precipitation.
Performance of supplementary effect is determined by precipitation pattern.
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