I was introduced to this exciting and growing field of nonlinear dynamical systems during my PhD which I started in September 2001 at the University of Agriculture, Abeokuta, Nigeria. I had earlier done some calculations in condensed matter; basically on the structural properties of undercooled Alkali metals using the Hybridized Mean Spherical Approximation (HMSA) during my Bachelors project. I was highly motivated by the results that I obtained from the calculation; and decided to pursue further research in this area. However, as time evolved, I came to realize that these assumptions could no longer hold, mainly due to the fact that Prof. Olatunde Akinlades' interest shifted from electronic structure calculations to nonlinear dynamics. Consequently, I was faced with the challenge of exploring this emerging area, practically thrown into the wilderness of chaos and its complexities.

My first challenge was choosing a research direction and topic - this was nontrivial, since I had no previous knowledge at all. After much study and research, I stumbled on control and synchronization � which have formed the framework of my current research focus. The idea of synchronization is that two interacting oscillators could entrain or be in-phase, whether periodic of chaotic. During synchronization, the dynamics of the interacting systems may be altered significantly. Control on the other hand, can be used to achieve a synchronization goal. These two are complimentary; and have several physical, chemical, biological and biomedical applications.

In my studies, I interpret these phenomena in the context of transport processes in non-equilibrium systems and in particular, the current transport and current reversals in inertia deterministic ratchets. Our recent results have revealed that the synchronization phenomenon could be employed in controlling directed transports arising from multi-stable states in the inertia ratchets. This result which we first reported in a series of papers namely, Phys. Lett. A 393 (2007) 91 and Physica A 384 (2007) 230, Physica D 231 (2007) 130 and Acta Physica Polonica B 38 (2007) 2459, has drawn research attention. A challenging problem is the design of cost effective and simple synchronization schemes [Phys. Scr. 79 (2009) 035801] that will achieve the goal of transport control in ratchet systems.

Since transport phenomena and in particular, directed transport are at the heart many problems in physics, chemistry and biology; and arises from the theme of ratchet physics where unbiased, noise induced transport emerges far from equilibrium due to the action of Brownian motors, the challenge of modelling and controlling some biological processes both at micro and macro scales has motivated research activities in inertia ratchets. Another source of motivation is the potential for technological applications aimed at devising mechanisms for sorting, separating pumping and controlling tiny particles at nano-scales. This also includes the control of motion of vortices in superconductors, particles in asymmetric silicon pores etc.

With these motivations, I joined the Nonlinear Biomedical Physics Group at Lancaster University in April, 2009, after spending one year as Alexander von Humbolt Fellow at the Institut für Theoretische Physik, Technische Univerisität Clausthal, Germany. My research work is currently sponsored by the Royal Society of London, the British Academy and the Royal Academy of Engineering through the prestigious Newton International Fellowship scheme. In my ongoing project, I treat the ratchet problems by considering coupled inertia ratchets that interacts via nonlinear and linear elastic and non-elastic-type of interactions that model real interactions in biological systems. It appears that such system can well describe the dynamics of actin-myosin in the muscle. Here, the aim is to understand the dynamic behaviour of coupled particles, by exploring the influence of different kinds of interactions on the transport properties. The underlying dynamical changes as well as the synchronization behaviour is also been investigated. On another scale, we also investigate the effect of a bath (a non-oscillatory force) and small parametric modulation control on the transports properties. The mechanism of parametric modulation is explored in various ways. This technique has already been realized experimentally for some systems and we believe that the effective realization of parametric control in ratchet models would provide information for experimental control of biological processes.

While here at Lancaster, I started to develop some interest on cardiovascular dynamics which Aneta Stefanovska is studying. It is highly fascinating that using ideas from nonlinear dynamics, one can obtain relevant information regarding the interaction mechanisms in living systems; and these could be useful for the early diagnosis and possibly, treatment of cardiac diseases.