The use of Pyragas-Type controller proved interest in the stabilization of unstable periodic orbits. The stabilization problem of a balancing inverted pendulum on an horizontally moving cart by the use of such a controller is considered. The main objective of the paper is to propose delayed control law containing only proportional gains able to stabilize the inverted pendulum by avoiding the ex...

In this paper, the general framework for calculating stability of equilibria, Hopf bifurcation a delayed prey-predator system with an SI type disease in prey population, is investigated. The impact incubation period delay on transmission utilizing nonlinear incidence rate was taken into account. For purpose explaining predation process, modified Holling II functional response used. First, exist...

This article concerns the dynamical behavior for a reaction-diffusion equation with integral term. First, by using bifurcation analysis and center manifold theorem, existence of periodic steady-state solution are established special kernel function general respectively. Then, we prove model admits traveling wave solutions connecting this steady state to uniform u=1 applying reduction phase diag...

We prove analogs of Thom’s transversality theorem and Whitney’s theorem on immersions for pseudo-holomorphic discs. We also prove that pseudo-holomorphic discs form a Banach manifold. MSC: 32H02, 53C15.

The discrete-time system has more complex and chaotic dynamical behaviors as compared to the continuous-time system. This paper extends a discrete Leslie–Gower predator-prey with Allee effect in predator’s population, whose dynamics are analyzed explored. We have determined equilibrium points studied their local stability properties. find that undergoes flip bifurcation Neimark–Sacker around in...

*Correspondence: [email protected] Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, P.R. China Abstract In this paper, the Hopf bifurcation control for a Lotka-Volterra predator-prey model with two delays is studied by using a hybrid control strategy. By analyzing the associated characteristic equation, its local stability and the exi...

We prove versions of various standard inequalities in which the dependence of the constant on the metric is explicit. 1 Technical results Definition. Let (M, g) be a smooth Riemannian n-manifold and let x ∈ M . Given Q > 1, k ∈ N, and p > n, the (Q, k, p)-harmonic radius at x, rH(Q, k, p)(x), is the supremum of reals r such that, on the geodesic ball Bx(r) of center x and radius r, there is a h...

The Whitham equation is a nonlocal shallow water-wave model which combines the quadratic nonlinearity of KdV with linear dispersion full water wave problem. conjectured existence highest, cusped, traveling-wave solution, and his conjecture was recently verified in periodic case by Ehrnstr\"om Wahl\'en. In present paper we prove it for solitary waves. Like case, proof based on global bifurcation...

a famous theorem of schur states that for a group $g$ finiteness of $g/z(g)$‎ ‎implies the finiteness of $g'.$ the converse of schur's theorem is an interesting problem which has been considered by some‎ ‎authors‎. ‎recently‎, ‎podoski and szegedy proved the truth of the converse of schur's theorem for capable groups‎. ‎they also established an explicit bound for the index of the...

A Riemann-Roch theorem asserts that some algebraically defined wrong– way map in K-theory agrees with a topologically defined one [BFM]. Bismut and Lott [BiLo] proved a Riemann–Roch theorem for smooth fiber bundles in which the topologically defined wrong–way map is the homotopy transfer of Becker–Gottlieb and Dold. We generalize their theorem, refine it, and prove a converse stating that an ap...