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The external term in [20] is supposed to belong to and to be almost periodic function.
The same holds for the external term V k ( ext ) ( τ k ( t, ω ), t, ω ).
For a fixed external term, take the symbol space, the set contains all translations of in.
We have included the leak reversal potential term in this "external" term for convenience.
A forced horizontal external term is added to the parametrically excited system.
In order to obtain the uniform attractor of the family of processes, we suppose the external term is locally asymptotic smallness (see Definition 4.5).
Similar(45)
Imagine him or her as you have seen the first subject: in physical, external terms.
The sum of the synaptic and external terms gives the deterministic contribution in the membrane potential.
This sort of dynamical systems can be generated by differential equations with both non-autonomous deterministic and stochastic external terms.
Motivated by this, we will prove that the process corresponding to problem (1.1)–(1.3) with external terms being locally asymptotic smallness (see Definition 4.5) possesses a compact uniform attractor in, which coincides with uniform attractor of the family of processes with external terms belonging to weak closure of translation set of locally asymptotic smallness function in.
Since the locally asymptotic smallness functions are not necessary to be translation compact in, compared with [20], the conditions on external terms of (1.1)–(1.3) can be relaxed in this paper.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com