Offset parameter cancellation produces countless coexisting attractors.

The average value of a system variable determines the position of its attractor. When the offset parameters come together and get disappeared after an algebraic operation, the location of the attractor is then governed by an initial condition only. In this case, parameter-dominated offset control turns out to be the initial condition-defined coexisting attractors. In this Letter, a special mechanism for generating countless coexisting attractors is disclosed. Furthermore, a new regime of multistability is revealed, which explains where and how countless coexisting attractors are born and arranged.

Dynamics editing based on offset boosting.

Multistability in a dynamical system has attracted great attention recently for its complex and unexpected states. Since in most chaotic systems coexisting attractors reside in their own individual basin of attraction with a fractal structure, it becomes a challenge to choose correct initial conditions to obtain desired dynamics. Selecting typical dynamics as the basic components in a dynamical sequence and then arranging them in the phase space in a desired order make the multistability transparent and controllable in the domain of initial conditions; thereafter, one can identify an attractor according to its initial sequence. Dynamics editing provides an effective technique to select typical attractors under different system parameters to form a flexible sequence in the phase space, which shows great potential for chaos-based secure communications.

[Effect of HBP-A on meniscal injury and pathological hypertrophy and calcification of the meniscus].

OBJECTIVE: To investigate the effect of HBP-A on meniscal injuries and the expressions of genes associated with pathological hypertrophy and calcification of the meniscusinduced by abnormal loading. METHODS: Bovine meniscus explants were subjected to 25% strain at 0.3 Hz for 3 h and treated with 0.6 mg/mL of HBP-A. The cell viability in the meniscus explants after 72 hin culture was determined using live/dead staining and the expression levels of genes associated with pathological hypertrophy and calcification of the meniscus (ANKH, ENPP1, ALP, MMP13, and IL-1) were measured using real-time PCR and Western blotting. The conditioned medium was collected for testing sulfated glycosaminoglycan (GAG) release. RESULTS: The number of dead cells, loss of proteoglycan content, and the expressions of ANKH, ENPP1, ALP and MMP13, and IL-1 at both the mRNA and protein levels were all significantly lower in the meniscus explants treated with 0.6 mg/mL HBP-A than in the explants with only 25% abnormal pressure stimulation (n=3, P<0.05). CONCLUSION: HBP-A can effectively alleviate meniscal injuries induced by abnormal loading and suppress the expressions of genes related with pathological hypertrophy and calcification of the meniscus, and can serve as a potential drug for treatment of knee osteoarthritis.