Her main research interest is the asymptotic theory of dissipative vortices (aka spiral/re-entrant waves/reentries) and its applications.

Among Dr Biktasheva's main theoretical achievements are the discovery and explanation of the macroscopic dissipative wave-particle duality of spiral waves (Phys Rev E, 67: 026221, 2003), quantitative prediction of stationary orbits for the drift of spiral waves around localised inhomogeneities (cover picture of Phys Rev Lett 104: 2010), and prediction of the drift of dissipative vortices caused by small variations of thickness in thin layers (Phys Rev Lett, 114: 068302, 2015). This recent progress in the quantitative understanding and prediction of dynamics of dissipative vortices in biological, physical and chemical media, most importantly in bio-medical applications, makes it close to a significant impact in many areas of science, medicine, and technology as never before, because the re-entrant waves represent e.g. (pathological) regimes of self-organisation, and transition to chaos, in cardiac (fibrillation) and brain (stroke and migraine) tissues, where the possibility of an effective control is of vital importance, with the high impact expected in, for example, improved cardiac ablation and implantable defibrillators. Drift of cardiac arrhythmia reentries due to their interaction with morphology of the heart clarifies now the role of anatomy of the organ, as well as that of a patient specific ischaemic zones. On the other end of the scale are the classic re-entrant waves of epidemics, and the re-entrant weather fronts, aka “low pressure systems”: storms and hurricanes in the atmospheric layer, underlying and manifesting climate change. The weather forecast dimensionality reduction from supercomputer PDEs to ODEs of the wave-particle trajectories of major storms and hurricanes, enhances timeliness and accuracy of forecast for a potential wind damage and/or flooding.

In April 2020, Dr Biktasheva's latest paper "Role of a Habitat's Air Humidity in Covid-19 Mortality" (Sci. Total Environ., 736: 138763, 2020) was submitted to UK Parliament and Government surveys on expert insights around the short, medium and long-term concerns and issues relating to COVID-19 and its impacts. It also received immediate worldwide attention.