Maynardgibbs1678

We investigate a network of excitable nodes diffusively coupled to their neighbors along four orthogonal directions. This regular network effectively forms a four-dimensional reaction-diffusion system and has rotating wave solutions. We analyze some of the general features of these hyperscroll waves, which rotate around surfaces such as planes, spheres, or tori. The surfaces evolve according to local curvatures and a system-specific surface tension. They have associated local phases and phase gradients tend to decrease over time. We also discuss the robustness of these network states against the removal of random node connections and report an example of hyperscroll turbulence.Potassium ion and sodium ion channels play important roles in the propagation of action potentials along a myelinated axon. The random opening and closing of ion channels can cause the fluctuation of action potentials. In this paper, an improved Hodgkin-Huxley chain network model is proposed to study the effects of ion channel blocks, temperature, and ion channel noise on the propagation of action potentials along the myelinated axon. It is found that the chain network has minimum coupling intensity threshold and maximum tolerance temperature threshold that allow the action potentials to pass along the whole axon, and the blockage of ion channels can change these two thresholds. A striking result is that the simulated value of the optimum membrane size (inversely proportional to noise intensity) coincides with the area range of feline thalamocortical relay cells in biological experiments.The superconducting Josephson junction shows spiking and bursting behaviors, which have similarities with neuronal spiking and bursting. This phenomenon had been observed long ago by some researchers; however, they overlooked the biological similarity of this particular dynamical feature and never attempted to interpret it from the perspective of neuronal dynamics. In recent times, the origin of such a strange property of the superconducting junction has been explained and such neuronal functional behavior has also been observed in superconducting nanowires. The history of this research is briefly reviewed here with illustrations from studies of two junction models and their dynamical interpretation in the sense of biological bursting.Foot-and-mouth disease is a highly contagious and economically devastating disease of cloven-hoofed animals. The historic occurrences of foot-and-mouth diseases led to huge economic losses and seriously threatened the livestock food security. In this paper, a novel age-space diffusive foot-and-mouth disease model with a Dirichlet boundary condition, coupling the virus-to-animals and animals-to-animals transmission routes, has been proposed. The basic reproduction number R0 is defined as the spectral radius of a next generation operator K, which is calculated in an explicit form, and it serves as a vital value determining whether or not the disease persists. The existence of a unique trivial nonconstant steady state and at least one nonconstant endemic steady state of the system is established by a smart Lyapunov functional and the Kronoselskii fixed point theorem. An application to a foot-and-mouth outbreak in China is presented. find more The findings suggest that increasing the movements and disinfection of the environment for animals apparently reduce the risk of a foot-and-mouth infection.In this paper, the transient response of the time-delay system under additive and multiplicative Gaussian white noise is investigated. Based on the approximate transformation method, we convert the time-delay system into an equivalent system without time delay. The one-dimensional Ito stochastic differential equation with respect to the amplitude response is derived by the stochastic averaging method, and Mellin transformation is utilized to transform the related Fokker-Planck-Kolmogorov equation in the real numbers field into a first-order ordinary differential equation (ODE) of complex fractional moments (CFM) in the complex number field. By solving the ODE of CFM, the transient probability density function can be constructed. Numerical methods are used to ascertain the effectiveness of the CFM method, the effects of system parameters on system response and the level of error vary with time as well as noise intensity are investigated. In addition, the CFM method is first implemented to analyze transient bifurcation, and the relation between CFM and bifurcation is discussed for the first time. Furthermore, the imperfect symmetry property appear on the projection map of joint probability density function.Understanding key patterns in a spatially extended system is an essential task of modern physics of complex systems. Just like in low-dimensional nonlinear systems, here we show that orbit topology plays a critical role even for the investigation of spatiotemporal dynamics. First, we design a new scheme to reduce possible continuous symmetries that are prevailing in these systems based on topological consideration. The scheme is successfully demonstrated in the well-known pattern formation systems. Interesting bifurcation routes to chaos are conveniently revealed after symmetry reduction. In particular, we find that near the onset of turbulent dynamics, with an increase of instability, local phase chaos with the same spatial topological index may merge into more complex ones, while those with different indices induce defect chaos necessarily through connections docked with defects. The topological argument is so strong that the scenario presented here should be omnipresent in diverse systems.The interconnectivity between constituent nodes gives rise to cascading failure in most dynamic networks, such as a traffic jam in transportation networks and a sweeping blackout in power grid systems. Basin stability (BS) has recently garnered tremendous traction to quantify the reliability of such dynamical systems. In power grid networks, it quantifies the capability of the grid to regain the synchronous state after being perturbated. It is noted that detection of the most vulnerable node or generator with the lowest BS or N-1 reliability is critical toward the optimal decision making on maintenance. However, the conventional estimation of BS relies on the Monte Carlo (MC) method to separate the stable and unstable dynamics originated from the perturbation, which incurs immense computational cost particularly for large-scale networks. As the BS estimate is in essence a classification problem, we investigate the relevance vector machine and active learning to locate the boundary of stable dynamics or the basin of attraction in an efficient manner.