In this paper, a food chain system with ratio-dependent functional response, impulses,feedback controls and delays is studied. By using the theorem of coincidence degree, homotopy invariance property and Lyapunov’s approach, a set of sufficient conditions for ensuring the existence and stability of positive periodic solutions of the system are derived. The results extend some recent works.
The microelectronics area constantly demands better and improved circuit simulation tools. This is the reason that this article is to present a biparameter homotopy with automated stop criterion, which is applied to direct current simulation of multistable circuits. This homotopy possesses the following characteristics: symmetry axis, double bounding solution line, arbitrary initial and final points, and lessen the nonlinearities that exist in the circuit. Besides, this method will be exemplified and discussed by using a benchmark multistable circuit.
In this study, we prove a strong convergence of Noor type scheme for a uniformly L-Lipschitzian and asymptotically pseudocontractive mappings in the intermediate sense without assuming any form of compactness. Consequently, we also obtain a convergence result for the class of asymptotically strict pseudocontractive mappings in the intermediate sense. Our results are improvements and extensions of some of the results in literature.
By using the bifurcation theory of dynamical systems to the generalized KP equation, under different parametric conditions, various sufficient conditions to guarantee the existence of the solitary wave solutions, periodic cusp wave solutions and compactons solutions are given. Some exact explicit parametric representations of the above waves are determined.