SMOTE sampling in caret package in R when using caret packge in the trainControl you can use "smote" sampling.
what is the default parameters the train in caret are using for smote??
parameters such as: 
perc.over = 300, k = 8, perc.under = 100..
ctrl <- trainControl(method = "repeatedcv",
                     number = 10,
                     repeats = 10, 
                     search = "grid", 
                     returnData = TRUE,
                     returnResamp = "final",
                     savePredictions = "all",
                     classProbs = TRUE,
                     sampling = "smote",
                     summaryFunction = twoClassSummary,
                     selectionFunction = "best",
                     allowParallel = TRUE)

 A: I reproduced the example of https://topepo.github.io/caret/subsampling-for-class-imbalances.html and tried another one. Results are:
perc.over = 200
perc.under = 200
It seems that the parameters are those of usage of the function SMOTE in the DMwR documentation (pag. 82):

Usage
SMOTE(form, data, perc.over = 200, k = 5, perc.under = 200,
  learner = NULL, ...)

In usage k = 5, but I verified only perc.over and perc.under:
library(caret)
library(DMwR)

set.seed(2969)
imbal_train <- twoClassSim(10000, intercept = -20, linearVars = 20)
table(imbal_train\$Class)

set.seed(9560)
smote_train <- SMOTE(Class ~ ., data  = imbal_train)                         
table(smote_train\$Class)[2]

perc.over <- 100*(table(smote_train\$Class)[2]-table(imbal_train\$Class)[2])/table(imbal_train\$Class)[2]
perc.under <- 100*table(smote_train\$Class)[1]/(table(smote_train\$Class)[2]-table(imbal_train\$Class)[2])

perc.over = 200
perc.under = 200
set.seed(1234)
imbal_train <- twoClassSim(10000, intercept = -40, linearVars = 40)
table(imbal_train\$Class)

set.seed(5678)
smote_train <- SMOTE(Class ~ ., data  = imbal_train)                         
table(smote_train\$Class)

perc.over <- 100*(table(smote_train\$Class)[2]-table(imbal_train\$Class)[2])/table(imbal_train$Class)[2]
perc.under <- 100*table(smote_train\$Class)[1]/(table(smote_train\$Class)[2]-table(imbal_train\$Class)[2])

perc.over = 200
perc.under = 200
