The coexisting oscillations are observed with a memcapacitor-based circuit that consists of two linear inductors, two linear resistors, and an active nonlinear charge-controlled memcapacitor. We analyze the dynamics of this circuit and find that it owns an infinite number of equilibrium points and coexisting attractors, which means extreme multistability arises. Furthermore, we also show the stability of the infinite many equilibria and analyze the coexistence of fix point, limit cycle, and chaotic attractor in detail. Finally, an experimental result of the proposed oscillator via an analog electronic circuit is given.

Analyzing the intrinsic dynamic characteristics of protein pockets is a key aspect to understanding the functional mechanism of proteins, which is conducive to the discovery and development of drugs. At present, the research on the dynamic characteristics of pockets mainly focuses on pocket stability, similarity, and physicochemical properties. However, due to the high complexity and diversity of high-dimensional pocket data in dynamic processes, this work is challenging. In this paper, we explore the dynamic characteristics of protein pockets based on molecular dynamics (MD) simulation trajectories. First, a dynamic pocket shape representation method combining topological feature data is proposed to improve the accuracy of pocket similarity calculation. Secondly, a novel high-dimensional pocket similarity calculation method based on pocket to vector dynamic time warp (P2V-DTW) is proposed to solve the correlation calculation problem of unequal length sequences. Thirdly, a visual analysis system of protein dynamics (VAPPD) is proposed to help experts study the characteristics of high-dimensional dynamic pockets in detail. Finally, the efficiency of our approach is demonstrated in case studies of GPX4 and ACE2. By observing the characteristic changes of pockets under different spatiotemporal scales, especially the motion correlation between pockets, we can find the allosteric pockets. Experts in the field of biomolecules who cooperated with us confirm that our method is efficient and reliable, and has potential for high-dimensional dynamic pocket data analysis.

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