No, why?
A resistor is a device whose state is defined by the current values of voltage and current.
That's it.
It applies to linear resistors, to symmetric nonlinear resistors (incandescent lamps), to asymmetric nonlinear resistors (diodes, LEDs...), etc.
Since at this point you appear to be trolling, let us cut through your trollish behavior.
Again with this trolling. Did you not see the reference I gave? Leon O. Chua is an authority in the field (I believe he was the one who postulated the existence of the memristor, he's the Chua of Chua's circuit). Both he and Charles A. Desoer taught at MIT. And MIT is the absolute excellence in the EE field. Do you think they are trolls?
Desoer and Kuh also wrote the previous high level bible of circuit theory, used in universities all over the world. No trolling, believe them.
You think that a resistor is defined upon its primary purpose. That's a nice definition for vocational school students. But when you raise the level and want to systematize the resolution of general nonlinear circuits containing any sort of elements you must be a little more cunning. You need to identify the true nature of a component from the point of view of the state variables. And this leads to generalization of concepts. As I said, there are four type of elements: resistors, capacitors, inductors and memristors. A diode? It's a nonlinear resistor. A varicap? It's a nonlinear capacitor. A Josephson junction? It's a nonlinear inductor.
And this is not classification per se: you need to place your elements variables in the correct part of the vector and matrices used to systematically solve these circuits. You don't have slots for diodes, Josephson junctions and so on. You have elements that depends on certain quantities, their derivatives or integrals.
I acknowledge that, so far, the majority of members seem to think that diodes are not resistors, it's fine. I am a bit puzzled by the lack of stance on the existence of nonlinear resistor according to them.
Do nonlinear resistors exists? And why can't they have an exponential VI characteristic?