An organic memristor/memcapacitor device comprises a biomimetic membrane attached on the surface of an electrode forming variable size toroidal matrix cross-linked to derivative cyclodextrin polymers forming cross bars, that facilitate a dual functioning biosensor characteristics which enabled to detecting voltage and current changes of a biomarker β-amyloid (Aβ) in pM concentration that direct linked to Alzheimer's disease and other neurodegenerative diseases under reagent-less, tracer-free and antibody-free conditions in biological fluid specimens.