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Such changes can be well approximated as impulses, and these processes tend to be reasonably modeled by impulsive differential equations.
Such interventions can be mathematically modeled by impulsive systems.
These complex dynamic behaviors can be modeled by impulsive differential systems.
These processes tend to be more suitably modeled by impulsive differential equations, which allow for discontinuities in the evolution of the state.
There are many physical phenomena that are described by means of impulsive differential equations, for instance, biological systems, electrical engineering, chemical reactions, among others can be modeled by impulsive differential equations, a good survey on impulsive differential equations can be found in [1] see also [2, 3].
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Recently, the state-dependent feedback control, which is modeled by the impulsive semi-dynamic systems, has become a hot topic and has been applied in other fields and science [14 18], and it suggests that the control tactics should only be applied once the states of model reach a prescribed given threshold.
In this section, a periodic impulsive switched predator-prey system with hibernation and birth pulse is modeled by the nonlinear impulsive differential equation left { textstylebegin{array}{l} left.
In sharp contrast to the thermal noise that is usually modeled by Gaussian noise, impulsive noise is another commonly encountered channel noise in various systems which involves instantaneous or impulse-like sharp sounds [6, 7].
The dynamics of observer state of the proposed AIO is modelled by an impulsive differential equation, by which the observer state is updated in an impulsive fashion.
The system under consideration is modeled by means of an impulsive subsystem, and the network-induced imperfections like packet dropout and delay are described by a Bernoulli distributed white sequence.
Figure 2 provides the theoretical and the simulated BER versus the SNR ratio for a 2×2 MIMO system with different modulation order in the presence of an impulsive noise modeled by the Cauchy law.
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