We prove a direct analogue of the classical Duflo formula in the case of L∞algebras. We conjecture an analogous formula in the case of an arbitrary Q-manifold. When G is a compact connected Lie group, the Duflo theorem for the Q-manifold (ΠTG, dDR) is exactly the Duflo theorem for the Lie algebra g = LieG. The corresponding theorem for the Q-manifold (ΠTM,dDR), where M is an arbitrary smooth ma...

We consider the diffusive single species growth in a plug flow reactor model with distributed delay. For small delay, existence and uniqueness of such wavefronts are proved when the convolution kernel assumes the strong generic delay kernel. The approaches used in this paper are geometric singular perturbation theory and the center manifold theorem.

A three-dimensional bio-reactor model of exploitative competition of two predator organisms with inhibition responses for the same renewable organism with reproductive properties is considered. By using a Lyapunov function and the center manifold theorem the global stability, the existence of Hopf bifurcation and limit cycles are proved. This result is useful in understanding the nonlinear osci...

Normal form theory is very important and useful in simplifying the forms of equations restricted on the center manifolds in studying nonlinear dynamical problems. In this paper, using the center manifold theorem associated with the integrated semigroup theory, we develop a normal form theory for semilinear Cauchy problems in which the linear operator is not densely defined and is not a Hille–Yo...

Abstract In this paper, the Hopf bifurcation and Turing instability for a mussel–algae model are investigated. Through analysis of corresponding kinetic system, existence stability conditions equilibrium type studied. Via center manifold theorem, sufficient in limit cycles obtained, respectively. addition, we find that strip patterns mainly induced by spot numerical simulations. These provide c...

the main objective of this paper is to find the necessary and sufficient condition of a given finslermetric to be einstein in order to classify the einstein finsler metrics on a compact manifold. the consideredeinstein finsler metric in the study describes all different kinds of einstein metrics which are pointwiseprojective to the given one. this study has resulted in the following theorem tha...

Moduli spaces M of self-dual SU(2) connections (“instantons”) over a compact Riemannian 4.manifold (hl, g) carry a natural L2 metric g, which is generally incomplete. For instantons of Pontryagin index 1 over a compact, simply connected, oriented, positive-definite base manifold, the completion M is Donaldson’s compactification; in fact the boundary of the completion is an isometric copy of (M,...

This article is about the dynamics of a discrete-time prey-predator system with Allee effect and immigration parameter on prey population. Particularly, we study existence local asymptotic stability unique positive fixed point. Furthermore, conditions for bifurcation in are derived. In addition, it shown that goes through period-doubling by using theory center manifold theorem. Eventually, nume...

This paper, according to the process of capital return, establishes a differential dynamics model investment with two time delays. When both delays are zero, it is proved that positively invariant, uniformly bounded, and globally asymptotically stable by using comparison principle Bendixson–Dulac theorem. at least one delay not Hopf bifurcation theorem, conditions local asymptotic stability exi...

A stage-structured predator-prey system with two time delays is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated and the existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory ...