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2010
Dynamical systems with delay (which we simply designate hereafter as delay dynamical systems or delay systems) are abundant in nature. They occur in a wide variety of physical, chemical, engineering, economic and biological systems and their networks. One can cite many examples where delay plays an important role.
M. Lakshmanan, D.V. Senthilkumar
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Dynamical systems with delay (which we simply designate hereafter as delay dynamical systems or delay systems) are abundant in nature. They occur in a wide variety of physical, chemical, engineering, economic and biological systems and their networks. One can cite many examples where delay plays an important role.
M. Lakshmanan, D.V. Senthilkumar
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2012
In this chapter we study general non-autonomous delay differential equations of the form $$\dot{x}(t) = F(t,x(t),x(t - \rho (t))).$$ Our intention is to demonstrate how pullback attractors can be used to investigate the behaviour of such models.
Alexandre N. Carvalho +2 more
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In this chapter we study general non-autonomous delay differential equations of the form $$\dot{x}(t) = F(t,x(t),x(t - \rho (t))).$$ Our intention is to demonstrate how pullback attractors can be used to investigate the behaviour of such models.
Alexandre N. Carvalho +2 more
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Metastability for delayed differential equations
Physical Review E, 1999In systems at phase transitions, two phases of the same substance may coexist for a long time before one of them dominates. We show that a similar phenomenon occurs in systems with delayed feedback, where short-term stable oscillatory patterns can also have very long lifetimes before vanishing into constant or periodic steady states.
C, Grotta-Ragazzo +2 more
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Delayed Differential Equations
2014Matematik olaylarıx'(t) = f(t, x(t ...
GÖZÜKIZIL, Ömer, Şencan, Huri
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Delays and Differential Delay Equations
1998Mathematically speaking, the most important tools used by the chemical kineticist to study chemical reactions like the ones we have been considering are sets of coupled, first-order, ordinary differential equations that describe the changes in time of the concentrations of species in the system, that is, the rate laws derived from the Law of Mass ...
Irving R. Epstein, John A. Pojman
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2011
Periodic motions in DDE (Differential-Delay Equations) are typically created in Hopf bifurcations. In this chapter we examine this process from several points of view. Firstly we use Lindstedt’s perturbation method to derive the Hopf Bifurcation Formula, which determines the stability of the periodic motion.
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Periodic motions in DDE (Differential-Delay Equations) are typically created in Hopf bifurcations. In this chapter we examine this process from several points of view. Firstly we use Lindstedt’s perturbation method to derive the Hopf Bifurcation Formula, which determines the stability of the periodic motion.
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Stochastic Delay Differential Equations
2021Real biological systems are always exposed to influences that are not completely understood or not feasible to model explicitly, and therefore, there is an increasing need to extend the deterministic models to models that embrace more complex variations in the dynamics. A way of modeling these elements is by including stochastic influences or noise.
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Fuzzy delay differential equations
Fuzzy Optimization and Decision Making, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lupulescu, Vasile, Abbas, Umber
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Vector Delay Differential Equations
2012Chapter 9 is devoted to nonoscillation of systems of delay differential equations. Wazewski’s result claims that a solution of the vector differential equation is not less than a solution of the differential inequality if and only if the off-diagonal entries of the matrix are nonpositive.
Ravi P. Agarwal +3 more
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