Abstract. This paper will present a path planning technique for autonomous mobile robot, based on the representation of the environment as a cognitive map through a spiking neural network (SNN) of O’Keefe place cells. The method is based on the concept of the travelling wave. For this purpose, we use a biologically plausible neural model (Izhikevitch model) which is the medium of a travelling w...

In this paper we investigate the existence of travelling wave solutions for a chemotaxis model under the scenarios of zero growth and constant growth rate. We use Lie symmetry analysis to generate generalized travelling wave solutions, a wider class of solutions than that obtained from the standard ansatz. Unlike previous approaches, we allow for diffusivity and signal degradation. We study the...

A two-dimensional micro-scale model for crystal dissolution and precipitation in a porous medium is presented. The local geometry of the pore is represented as a thin strip. The model allows for changes in the pore volume. A formal limiting argument leads to a system of 1D effective upscaled equations. The effective equations allow for travelling wave solutions. Existence and uniqueness of thes...

An extended ( ′ G )–expansion method is obtained by improving the form of solution in ( G′ G )– expansion method which is proposed in recent years. By using the extended ( ′ G )–expansion method and with the aid of homogeneous balance principle, many explicit and exact travelling wave solutions with two arbitrary parameters to the Klein-Gordon equation are presented, including the hyperbolic so...

We theoretically discuss the impact of the cavity configuration on the possible longitudinal mode multistability in homogeneously broadened lasers. We present a general method allowing to perform a direct bifurcation diagram and to determine the stability of the solutions of a Travelling wave model. We find, in agreement with recent experimental reports, that multistability is more easily reach...

In this paper, we use the phase plane method for finding finite travelling waves solutions for the diffusion-absorption-convection equation ut = A(|ux|ux)x + B(u)x − Cu , (x, t) ∈ R× R. We show that the existence of solutions which depends on the parameters p, q and n. Also we study the asymptotic behavior of these solutions.

The simplest equation method presents a wide applicability to handling nonlinear wave equations. In this paper, we establish travelling wave solutions for some nonlinear evolution equations. The simplest equation method is used to construct the travelling wave solutions of new Hamiltonian amplitude equation, (3 + 1)-dimensional generalized KP equation, Burgers-KP equation, coupled Higgs field e...

We are investigating possible functional roles for spiral wave activity in visual cortex. Our initial findings suggest that spiral wave formation could contribute to visual salience analysis, in particular for mediating attention to human body features. Exploiting travelling wave dynamics for visual processing offers many advantages, including template-free sensitivity to spatial patterns, robu...