No abstract

The title eremophilenolide, C15H22O3, is a natural compound isolated from Senecio laetus Edgew. The two cis-fused six-membered rings have chair confomations and the five-membered ring has a planar envelope conformation [maximum deviation = 0.010 (1) Å]. The β-hy­droxy group participates in inter­molecular O—H⋯O hydrogen bonding, forming mol­ecular chains along the a axis.

One type of tree-grass competition model with cross-diffusion is analyzed in this paper. Firstly, according to the distribution theory of the roots of the characteristic equation, the existence and stability conditions of the positive equilibrium point are obtained, and the global stability of the system is proved by using the Bendixson–Dulac theorem. Secondly, we select the fire factor as the control parameter, and obtain the critical value of Turing bifurcation and the conditions of Turing pattern. Then, we derive the amplitude equation near the Turing bifurcation point by using the standard multiscale analysis method. Finally, we do a sensitivity analysis on the tree-grass system with the fire factor, and then a series of numerical simulations based on these analysis results are carried out to verify our theoretical analysis and Turing pattern structure, which is consistent with the biological significance of the tree-grass model.

In this paper, the Hopf-zero bifurcation of the ring unidirectionally coupled Toda oscillators with delay was explored. First, the conditions of the occurrence of Hopf-zero bifurcation were obtained by analyzing the distribution of eigenvalues in correspondence to linearization. Second, the stability of Hopf-zero bifurcation periodic solutions was determined based on the discussion of the normal form of the system, and some numerical simulations were employed to illustrate the results of this study. Lastly, the normal form of the system on the center manifold was derived by using the center manifold theorem and normal form method.