Keywords: Neutral delayed differential equation Double Hopf bifurcation Normal form Multiple time scales Center manifold reduction a b s t r a c t In this paper, we study dynamics in a container crane model with delayed position feedback , with particular attention focused on non-resonant double Hopf bifurcation. By using multiple time scales and center manifold reduction methods, we obtain the...

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,...

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...

Abstract Let d be a positive integer. We show finiteness theorem for semialgebraic $$\mathscr {RL}$$ RL triviality of Nash family functions defined on manifold, generalising Benedetti–Shiota’s equivalence classes appearing in the space real polynomial degree not exceeding . also prove Fukuda’s claim, Theorem ...

Building on results obtained in [ 21 ], we prove Local Stable and Unstable Manifold Theorems for nonlinear, singular stochastic delay differential equations. The main tools are rough paths theory a semi-invertible Multiplicative Ergodic Theorem cocycles acting measurable fields of Banach spaces 20 ].

Let M1 and M2 be two Kähler manifolds. We call M1 and M2 relatives if they share a non-trivial Kähler submanifold S, namely, if there exist two holomorphic and isometric immersions (Kähler immersions) h1 : S → M1 and h2 : S → M2. Moreover, two Kähler manifolds M1 and M2 are said to be weakly relatives if there exist two locally isometric (not necessarily holomorphic) Kähler manifolds S1 and S2 ...

Let M 1 and M 2 be two Kähler manifolds. We call M 1 and M 2 relatives if they share a non-trivial Kähler submanifold S, namely, if there exist two holomorphic and isometric immersions (Kähler immersions) h 1 : S → M 1 and h 2 : S → M 2. Moreover, two Kähler manifolds M 1 and M 2 are said to be weakly relatives if there exist two locally isometric (not necessarily holomorphic) Kähler manifolds ...

Higher-order time integration methods that unconditionally preserve the positivity and linear invariants of underlying differential equation system cannot belong to class general methods. This poses a major challenge for stability analysis such since new iterate depends nonlinearly on current iterate. Moreover, systems, existence is always associated with zero eigenvalues, so steady states cont...