An abstract existence result and its applications.
Bifurcation analysis in a kind of fourth-order delay differential equation.
Bifurcation analysis of a Kaldor-Kalecki model of business cycle with time delay.
Bifurcation analysis on a delayed SIS epidemic model with stage structure.
Dimensional reduction of nonlinear time delay systems.
Effective criterion for the transformation of linear functional-differential equations of first order into canonical form with constant coefficients and deviations
Equivalence and symmetries of first order differential equations
In this article, the equivalence and symmetries of underdetermined differential equations and differential equations with deviations of the first order are considered with respect to the pseudogroup of transformations
Global transformations of linear differential equations.
Modified Wiener equations.
Note on canonical forms for functional-differential equations.
On time transformations for differential equations with state-dependent delay
Systems of differential equations with state-dependent delay are considered. The delay dynamically depends on the state, i.e. is governed by an additional differential equation. By applying the time transformations we arrive to constant delay systems and compare the asymptotic properties of the original and transformed systems.
On transformations of functional-differential equations
Reductions and conservation laws for BBM and modified BBM equations
In this paper, the classical Lie theory is applied to study the Benjamin-Bona-Mahony (BBM) and modified Benjamin-Bona-Mahony equations (MBBM) to obtain their symmetries, invariant solutions, symmetry reductions and differential invariants. By observation of the the adjoint representation of Mentioned symmetry groups on their Lie algebras, we find the primary classification (optimal system) of their group-invariant solutions which provides new exact solutions to BBM and MBBM equations. Finally, conservation...
Remark to transformations of functional-differential equations of the first order
Smooth Gevrey normal forms of vector fields near a fixed point
We study germs of smooth vector fields in a neighborhood of a fixed point having an hyperbolic linear part at this point. It is well known that the “small divisors” are invisible either for the smooth linearization or normal form problem. We prove that this is completely different in the smooth Gevrey category. We prove that a germ of smooth -Gevrey vector field with an hyperbolic linear part admits a smooth -Gevrey transformation to a smooth -Gevrey normal form. The Gevrey order depends on...
Stability and bifurcation in a simplified four-neuron bam neural network with multiple delays.