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While the original goal for developing robots is replacing humans in dangerous and tedious tasks, the final target shall be completely mimicking the human cognitive and motor behavior. Hence, building detailed computational models for the human brain is one of the reasonable ways to attain this. The cerebellum is one of the key players in our neural system to guarantee dexterous manipulation and coordinated movements as concluded from lesions in that region. Studies suggest that it acts as a forward model providing anticipatory corrections for the sensory signals based on observed discrepancies from the reference values. While most studies consider providing the teaching signal as error in joint-space, few studies consider the error in task-space and even fewer consider the spiking nature of the cerebellum on the cellular-level. In this study, a detailed cellular-level forward cerebellar model is developed, including modeling of Golgi and Basket cells which are usually neglected in previous studies. To preserve the biological features of the cerebellum in the developed model, a hyperparameter optimization method tunes the network accordingly. The efficiency and biological plausibility of the proposed cerebellar-based controller is then demonstrated under different robotic manipulation tasks reproducing motor behavior observed in human reaching experiments.

When a system's activity alternates between a resting state (e.g. a stable equilibrium) and an active state (e.g. a stable periodic orbit), the system is said to exhibit bursting behavior. We use bifurcation theory to identify three distinct topological types of bursting in one-dimensional mappings and 20 topological types in two-dimensional mappings having one fast and one slow variable. We show that different bursters can interact, synchronize, and process information differently. Our study suggests that bursting mappings do not occur only in a few isolated examples, rather they are robust nonlinear phenomena.

The chaotic spiking and intermittent chaotic bursting were observed from biological experiment on a neural pacemaker. The intermittent chaotic bursting manifested alternation between a phase of nearly period-3 bursting and another phase of irregular bursting, and exhibited a nonsmooth-like structure in the first return map of interspike interval (ISI) series. The chaotic spiking manifested a smooth structure. The intermittent chaotic bursting and spiking simulated in the Chay model were identified by the dissection of the fast-slow variables. The intermittent chaotic bursting manifested nonsmooth-like structures in the first return map of both ISI and slow variable, while spiking exhibited smooth structures. The intermittent chaotic bursting and spiking manifested different scale laws of the averaged length of periodic phase with respect to the changes of parameter value. The scale law of bursting was similar to those of both type V intermittent chaos generated in a nonsmooth map and type I in a smooth system, while that of spiking resembled type I more than type V. The results revealed the dynamics of intermittent chaotic firing patterns, the differences between the intermittent chaotic bursting and spiking patterns and the relationships to the smooth and nonsmooth-like characteristics, provided a deep understanding of intermittent chaotic firing patterns, and indicated different mechanisms of the adjustment of variables from slow to fast between bursting and spiking patterns.

A slow-fast delay-coupled flexible joint system is investigated in this paper. To understand the effects of time delay on the stability and oscillation of the manipulator, the geometric singular perturbation method is extended in dealing with delay differential equations. Bogdanov–Takens (BT) bifurcation of the fast subsystem is obtained, which leads to the existence of homoclinic orbits and is proved to be related to the formation of spiking. After the break of homoclinic orbits, Melnikov theory is introduced to predict the threshold curve indicating the occurrence of chaos. Numerical results show that with the increase of time delay, the stability of the system gets worse, and complicated oscillations including bursting, chaotic-bursting and complete chaos turn up. Besides, it is briefly summarized that the effect of the small parameter in the slow-fast system is to influence the convergence rate of solution trajectories, which is widely neglected in previous works.