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Local dynamics of the model of a semiconductor laser with delay
We study a model of a semiconductor laser with delay. We discuss the stability of the equilibrium and single out bifurcation parameter values. It turns out that resultant critical cases have infinite dime...
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Local dynamics of equation with periodically distributed delay
We study an equation with periodically distributed delay. The dependence of the equilibrium state stability on the parameters is investigated. We show that the stability region can have a complicated shape...
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Article
Local Dynamics of a Singularly Perturbed Second Order Equation with State-Dependent Delay
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Dynamics of a singularly perturbed system of two differential equations with delay
We study a two-dimensional singularly perturbed system with delay, which is a simplification of models used in laser physics. We analyze several cases of a small parameter multiplying the derivative in th...
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Article
Influence of the Second Delay on Local Dynamics
The local dynamics of singularly perturbed equations with two delays are studied in the case when both delays are asymptotically large and identical in the order of magnitude (proportional). Critical cases are...
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Analysis of Local Dynamics of Difference and Close to Them Differential-Difference Equations
We study the local dynamics of one class of nonlinear difference equations which is important for applications. Using perturbation theory methods, we construct sets of singularly perturbed differential-differe...
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Local dynamics of a second-order differential-difference equation with large delay at the first derivative
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Local dynamics of an equation with two large different-order delays
The behavior of solutions near an equilibrium of differential equations with two large different-order delays is studied. In critical cases, special equations (namely, quasi-normal forms) determining the dynam...
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Local dynamics of an equation with a large state-dependent delay
The behavior of solutions to first- and second-order differential equations with a large state-dependent delay is analyzed in a neighborhood of equilibrium. In critical cases, it is shown that their behavior i...
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Dynamics of strongly coupled spatially distributed logistic equations with delay
The dynamics of a system of two logistic delay equations with spatially distributed coupling is studied. The coupling coefficient is assumed to be sufficiently large. Special nonlinear systems of parabolic equ...
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Influence of delayed feedback control on the stability of periodic orbits
A problem of stabilization of unstable cycles is solved in this paper using delay feedback at the example of a model equation with cubic nonlinearity. We consider the case when, in a problem without control, e...
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Multistability in a laser model with large delay
Dynamics of laser generation is considered on the base of single-mode rate equations with retarded argument. In the framework of local analysis, we determine continual sets of families of quasi-normal forms in...
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Dynamics of the logistic delay equation with a large spatially distributed control coefficient
The local dynamics of the logistic delay equation with a large spatially distributed control coefficient is asymptotically studied. The basic bifurcation scenarios are analyzed depending on the relations betwe...
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Local dynamics of an equation with large delay and distributed deviation of the space variable
We study the local dynamics in a neighborhood of an equilibrium state for an equation with delay in time and integral distribution in the space variable. In the close-to-critical cases depending on the relatio...
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Local dynamics of an equation with distributed delay
We study the properties of the local dynamics of a differential equation with a distributed delay. We consider two forms of distribution functions, exponential and linear. We indicate parameters for which crit...
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Spatial properties of high-mode bifurcations of distributed logistic equations
The local dynamics of the solution of spatially distributed logistic equations are studied. It is shown that critical cases in the problem of equilibrium stability have infinite dimension. New bifurcation phen...
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Quasi-normal forms of two-component singularly perturbed systems
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Quasi-normal forms for parabolic systems with strong nonlinearity and weak diffusion
The local dynamics of a system of parabolic equations with strong nonlinearity involving a spatial derivative are studied. The basic critical cases when an equilibrium state becomes unstable are discussed. In ...
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Asymptotic study of the corporate dynamics of systems of equations coupled by delay control
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Cooperative dynamics of strongly coupled distributed systems
