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Recently developed bioinspired robots imitate their live counterparts in both aspect and functionality. Nevertheless, whether these devices can be integrated within the ecological niche inspiring their design is seldom tested experimentally. An elemental research question concerns the feasibility of modulating spontaneous behaviour of animal systems through bioinspired robotics. The following study explores the possibility of engineering a robotic fish capable of influencing the behaviour of live zebrafish (Danio rerio) in a dichotomous preference test. While we observe that the preference for the robotic fish never exceeds the preference for a conspecific, our data show that the robot is successful in attracting both isolated individuals and small shoals and that such capability is influenced by its bioinspired features. In particular, we find that the robot's undulations enhance its degree of attractiveness, despite the noise inherent in the actuation system. This is the first experimental evidence that live zebrafish behaviour can be influenced by engineered robots. Such robotic platforms may constitute a valuable tool to investigate the bases of social behaviour and uncover the fundamental determinants of animal functions and dysfunctions.

Abstract. We investigate higher order matched asymptotic expansions of a steady-state Poisson-Nernst-Planck (PNP) system with particular attention to the I-V relations of ion channels. Assuming that the Debye length is small relative to the diameter of the narrow channel, the PNP system can be viewed as a singularly perturbed system. Special structures of the zeroth order inner and outer systems make it possible to provide an explicit derivation of higher order terms in the asymptotic expansions. For the case of zero permanent charge, our results concerning the I-V relation for two oppositely charged ion species are (i) the first order correction to the zeroth order linear I-V relation is generally quadratic in V; (ii) when the electro-neutrality condition is enforced at both ends of the channel, there is NO first order correction, but the second order correction is cubic in V. Furthermore (Theorem 3.4), up to the second order, the cubic I-V relation has (except for a very degenerate case) three distinct real roots that correspond to the bistable structure in the FitzHugh-Nagumo simplification of the Hodgkin-Huxley model. 1. Introduction. The Poisson-Nernst-Planck (PNP) systems are basic electro-diffusion equations modeling, for example, ion flow through membrane channels and transport of holes and electrons in semiconductors (see, for example, [3,4,5,10,21,32,39,18,19,34,35]). In the context of ion flow through a membrane channel, the flow of ions is driven by their concentration gradients and by the electric field modeled together by the Nernst-Planck continuity equations, and the electric field is in turn determined by the concentrations through the Poisson equation. The PNP system describes the current flow at low resolution; that is, it is an approximate description of the transport process [3] appropriate when channel selectivity (between different chemical species of ions) is not of importance, as, for example, in the numerous classical studies of the gramicidin channel [51] most recently reviewed in [1, 2] (see also [16,36,37,11,25,51,17,20]). Derivation from a Langevin model of ionic diffusion [42] shows how correlations are approximated in PNP systems and suggests extensions of the PNP approach to deal with selectivity arising from excess chemical potentials [13,14,6]. The bio-