No abstract

Pollinators use their sense of smell to locate flowers from long distances, but little is known about how they are able to discriminate their target odor from a mélange of other natural and anthropogenic odors. Here, we measured the plume from Datura wrightii flowers, a nectar resource for Manduca sexta moths, and show that the scent was dynamic and rapidly embedded among background odors. The moth's ability to track the odor was dependent on the background and odor frequency. By influencing the balance of excitation and inhibition in the antennal lobe, background odors altered the neuronal representation of the target odor and the ability of the moth to track the plume. These results show that the mix of odors present in the environment influences the pollinator's olfactory ability.

We consider a class of nonlinear Schrödinger / Gross-Pitaveskii (NLS-GP) equations, i.e. NLS with a linear potential. We obtain conditions for a symmetry breaking bifurcation in a symmetric family of states as N , the squared L 2 norm (particle number, optical power), is increased. In the special case where the linear potential is a doublewell with well separation L, we estimate N cr (L), the symmetry breaking threshold. Along the "lowest energy" symmetric branch, there is an exchange of stability from the symmetric to asymmetric branch as N is increased beyond N cr .

We develop a biophysical model of neurosensory integration in the model organism Caenorhabditis elegans. Building on experimental findings on the neuron conductances and their resolved connectome, we posit the first full dynamic model of the neural voltage excitations that allows for a characterization of network structures which link input stimuli to neural proxies of behavioral responses. Full connectome simulations of neural responses to prescribed inputs show that robust, low-dimensional bifurcation structures drive neural voltage activity modes. Comparison of these modes with experimental studies allows us to link these network structures to behavioral responses. Thus the underlying bifurcation structures discovered, i.e., induced Hopf bifurcations, are critical in explaining behavioral responses such as swimming and crawling.

No abstract

The truncated forced nonlinear Schrödinger (NLS) model is known to mimic well the forced NLS solutions in the regime at which only one linearly unstable mode exists. Using a novel framework in which a hierarchy of bifurcations is constructed, we analyze this truncated model and provide insights regarding its global structure and the type of instabilities which appear in it. In particular, the significant role of the forcing frequency is revealed and it is shown that a parabolic resonance mechanism of instability arises in the relevant parameter regime of this model. Numerical experiments demonstrating the different types of chaotic motion which appear in the model are provided.

No abstract

Three different types of chaotic behavior and instabilities (homoclinic chaos, hyperbolic resonance, and parabolic resonance) in Hamiltonian perturbations of the nonlinear Schrödinger (NLS) equation are described. The analysis is performed on a truncated model using a novel framework in which a hierarchy of bifurcations is constructed. It is demonstrated numerically that the forced NLS equation exhibits analogous types of chaotic phenomena. Thus, by adjusting the forcing frequency, the behavior near the plane wave solution may be set to any one of the three different types of chaos for any periodic box length.