BiographyAbdelhamid (Hamid) Ajbar earned his B.Sc degree (Ingenieur D’Etat) in chemical engineering from Ecole Nationale de L’Industrie Minerale, Morocco in 1988. He pursued his graduate studies in Notre Dame university in USA where he earned a master’s in Chemical Engineering in 1991 followed by a Ph.D in 1994. He worked in the area of process control under the supervision of Prof. Jeffrey Kantor. The Ph.D dissertation was on “Robust Control and Monitoring of Discrete Time Feedback Control Systems”. Currently he is a professor of chemial Engineering at King Saud University, Riyadh, Saudi Arabia. Dr. Ajbar published three books and over 50 refereed journal publications. He also supervised a number of master and Ph.D students. The King Saud University is one of the largest universities in the Middle East region and has shown tremendous research activities in the past years. My main research area is the nonlinear analysis of the bioreactors. The move from my primary reaserch area of process control to bifuraction analysis which resulted in the current book (Dynamics of the Chemostat: A Bifurcation Theory Approach, CRC Press) has a story. After my Ph.D (1994) I came across the work carried out since the eighties on the use of singulairty theory to analyze multiplicity phenomenon in the continuous stirred tank reactor, especillay the work carried out by Professors luss and Balakotaiah and by the late Professor Aris and his student Khalid Alhumaizi, who is also the co-author of this book. I realized that the singularity theory could be applied with greater success to examine the nonlinear features of the chemostat.
The first work was published in 1997 (Comput. Model., 25:31–48 (1997) with the cooperation of Dr. Gamal Ibrahim. Since then, I applied the singularity theory to the dynamics of the chemostat for various applications. The list below is the articles I published in the field. Most models I worked with are unstructured kinetic models that are described by simple ordinary differential equations. Sometimes the analysis can be deep and the results concerning the static bifurcation or the occurrence of periodic behavior in such models can be obtained for arbitrary functional responses.
Research Area: Bioreactor Dynamics
 A. Ajbar. Study of complex dynamics in pure and simple microbial competition, Chem. Eng. Sci. 80:188-194 (2012).
 E. Ali, A. Ajbar and K. Alhumaizi. Dynamics of recombinant DNA cultures under time varying feed conditions, Chem. Eng. Commun. 199: 1155-1168 (2012).
 A. Ajbar, M. AlAhmad and E. Ali. On the dynamics of biodegradation of wastewater in aerated continuous bioreactors, Mathl. Comput. Model. 54: 1930-1942 (2011).
 A. Ajbar. On the improvement of performance of bioreactors through periodic forcing. Comp. Chem. Eng. 35:1164-1170 (2011).
 A. Ajbar. Study of the operability of nonideal continuous bioreactors. Chem. Eng. Commun. 198:385–415 (2011).
 A. Al-Rabiah and A. Ajbar. Study of the operability of a continuous bioreactor for the pre- fermentation of cheese. Eng. Life. Sci., 8:157–166 (2008).
 K. Alhumaizi, A. Alwan and A. Ajbar. Competition of plasmid-bearing and plasmid-free organisms in a chemostat: A study of bifurcation phenomena. Math. Comput. Model. 44:342–367 (2006).
 K. Alhumaizi, E. Ali and A. Ajbar. Study of some unique features of ratio-dependent models for predator-prey-substrate interactions in continuous cultures. Chem. Eng. Commun. 193:1164–1184 (2006).
 K. Alhumaizi and A. Ajbar. Optimization of an unstructured first-order kinetic model of cyclically operated bioreactors. J. Env. Eng. 132:453-45 (2006).
 K. Alhumaizi and A. Ajbar. Dynamics of predator-prey interactions in continuous cultures. Eng. Life. Sci. 5:139–147 (2005).
 A. Ajbar. Classification of static and dynamic behavior in chemostat for plasmid-bearing, plasmid-free mixed recombinant cultures. Chem. Eng. Commun.,189:1130–1154 (2002).
 A. Ajbar and A.H. Fakeeha. Static and dynamic behavior of a class of unstructured models of continuous bioreactors with growth associated product. Bioprocess. Biosys. Eng. 25: 21-27 (2002).
 A. Ajbar. Classification of static and dynamic behavior in chemostat for plasmid-bearing, plasmid free mixed recombinant cultures. Chem. Eng. Commun. 189: 1130-1133 (2002).
 A. Ajbar. Classification of stability behavior of bioreactors with wall attachment and substrate-inhibited kinetics. Biotechnol. Bioeng. 72:166–176 (2001).
 A. Ajbar. Classification of static behavior of a class of unstructured models of continuous processes. Biotechnol. Prog. 17:597–605 (2001).
 A. Ajbar. On the existence of oscillatory behavior in unstructured models of bioreactors. Chem. Eng. Sci., 56:1991–1997 (2001).
 A. Ajbar. Operability of continuous bioprocesses: Static behavior of a large class of unstructured models. Eng. Life Sci., 1:187–196 (2001).
 A. Ajbar. Periodic behaviour of a class of unstructured kinetic models for continuous bioreactors. Can. J. Chem. Eng. 79:791–799 (2001).
 A. Ajbar. Stability analysis of the biodegradation of mixed wastes in a continuous bioreactor with cell recycle. Water Res. 35:1201–1208 (2001).
 A. Ajbar and K. Alhumaizi. Biodegradation of substitutable substrates in a continuous bioreactor with cell recycle: A study of static bifurcation. Math. Comput. Model. 31:159–174 (2000).
 A. Ajbar and K. Alhumaizi. Microbial competition: Study of global branching phenomena. AIChE J., 46:321–334 (2000).
 A.Ajbar and G. Ibrahim. Periodic and nonperiodic oscillatory behavior in a model for activated sludge reactors. Math. Comput. Modell. 25:9-12 (1997).
 A. Ajbar and G. Ibrahim Stability and bifurcation of an unstructured model of a bioreactor with cell recycle. Math. Comput. Model., 25:31–48 (1997).
Research Area: Chemical Process Dynamics
 A. Alhumaizi, A. Ajbar, and M.A. Soliman M.A. Modeling the complex interactions between reformer and reduction furnace in a Midrex-based iron plant, Can. J. Chem. Eng. 90: 1120-1141 (2012).
 E. Ali , A Ajbar and I. Almutaz, Periodic control of a reverse osmosis desalination process, J. Proc. Contr. 22: 218-227 (2012).
 A. Ajbar, K. Alhumaizi, and M.A. Soliman, Modelling and parametric studies of direct reduction reactor, Ironmak. Steelmak., 38:401-411 (2011).
 A. Ajbar, K. Alhumaizi and M. Soliman, Modeling and simulations of a reformer used in direct reduction of iron, Korean J. Chem. Eng. 28:2242-2249 (2011).
 A. Ajbar, Y. Bakhbakhi, S. Ali, M. Asif, Fluidization of nano-powders: Effect of sound vibration and pre-mixing with group A particles, Powder Technol. 36: 327-337 (2011).
 M. Al-haj Ali, A. Ajbar, E. Ali, K. Alhumaizi, Robust model-based control of a tubular reverse-osmosis desalination unit, Desalination, 255:129-136 (2010)
 M. Al-haj Ali, A. Ajbar, E. Ali, K. Alhumaizi, Modeling the transient behavior of an experimental reverse osmosis tubular membrane, Desalination, 245:194-204 (2009).
 A. Ajbar, W. Al-Masry, E. Ali, Prediction of flow regimes transitions in bubble columns using passive acoustic measurements, Chem. Eng. Proc. 48:101-110 (2009).
 A. Ajbar, K. Alhumaizi and M. Asif, Improvement of the fluidizability of cohesive powders through mixing with small proportions of group A particles. Can. J. Chem. Engng. 83:930-935 (2005).
 E. Ali, K. Alhuamizi and A. Ajbar, Multivariable control of a simulated industrial gas phase polyethylene reactor. Ind. Eng. Chem. Res., 42:2349-2351 (2003).
 A.Ajbar, K. Alhumaizi, I Aidid and M. Asif, Hydrodynamics of gas fluidized beds with mixture of group D and B particles, Can. J. Chem. Eng. 80:281:290 (2002).
 A. Ajbar, K. Alhumaizi, and S.S.E.H. Elnashaie. Classification of static and dynamic behavior in a fluidized-bed catalytic reactor. Chem. Eng. J., 84:503–516 (2001).
 A. Ajbar. Stabilization of chaotic behavior in a two-phase autocatalytic reactor, Chaos, Solitons and Fractals, 12:903-910 (2001).
 A. Ajbar and K. Alhumaizi. Gas phase polyethylene reactors: A global study of stability behaviour. Chem. Eng. Res. Des., 79:195–208 (2001).
 A. Alhusseini, and A. Ajbar, Mass Transfer in Supported Liquid Membranes: A Rigorous Model ., Math. Comp. Model. 32:465-460 (2000).
 E. Ali, K. Alhumaizi and A. Ajbar, Model reduction and robust control of multi-stage flash (MSF) desalination plants, Desalination, 121:65-67 (1999).
 E. Ali, A. Ajbar, and K. Alhumaizi, Robust control of industrial multi-stage flash desalination plants: , Desalination, 114, p. 289 (1997).
 S.S.E.H. Elnashaie and A. Ajbar, Period-adding and chaos in fluidized bed catalytic reactors. Chaos, Solitons & Fractals, 7, p. 1317 (1996).
 S.S.E.H. Elnashaie and A. Ajbar, Chaotic, non-chaotic strange attractors and bistability in non-isothermal fluidized bed catalytic reactors under PI control., Chaos, Solitons & Fractals, 7, p.1955 (1996).
 A. Ajbar and S.S.E.H. Elnashaie, Controlling chaos by periodic perturbations in nonisothermal fluidized-bed reactor, AIChE J., 42, p. 3008 (1996).
 H. Ajbar, M. R. Keenan and J. C. Kantor. Optimal linear regulation with hard constraints. AIChE J., 41, p. 2439 (1995).
 A. Ajbar, and J. C. Kantor, "Time Domain Approach to the Design of Integrated Control and Diagnosis Systems," " Modeling of Uncertainty in Control Systems," Springer-Verlag, , (1994), 337.
 Y. Bakhbakhi, S. Alfadul, A. Ajbar, Precipitation of Ibuprofen Sodium using compressed carbon dioxide as antisolvent, European Journal of Pharmaceutical Sciences (in press). http://dx.doi.org/10.1016/j.ejps.2012.10.013
 Y. Bakhbakhi. M. Asif, A. Chafidz and A. Ajbar, Formation of biodegradable polymeric fine particles by supercritical antisolvent precipitation process. Polym. Eng. Sci.DOI: 10.1002/pen.23301
 F. AlMubaddal, K. AlRumaihi, A. Ajbar, Performance optimization of coagulation/flocculation in the treatment of wastewater from a polyvinyl chloride plant, J. Hazrd.Mat.161, p.431(2009).
 I. Almutaz, A. Ajbar, Y. Khalid and E. Ali, A probabilistic forecast of water demand for a tourist and desalination dependent city: Case of Mecca, Saudi Arabia, Desalination, 294, p.53(2012).
 I. Almutaz, A. Ajbar and E. Ali Determinants of residential water demand in an arid and oil rich country: A case study of Riyadh city in Saudi Arabia IJPS (in press).
Areas of Research / Professional Expertise
My scientific research is centered around two areas:
1- Bifurcation analysis of chemostat models: The primary aim of my work is to generate analytical (if possible) solutions to nonlinear patterns that exist in the chemostat. Most models I worked with are unstructured kinetic models that are described by two to three ordinary differential equations. These models are generally amenable to analytical manipulations. Elements of bifurcation theory (e.g. singularity) can be used to study the branching phenomena that my exist in such models. Sometimes the analysis can be carried out for arbitrary specific growth rates (i.e. functional responses). The occurrence of oscillatory behavior in such models is always interesting to investigate. In a number of cases involving interactions between species (e.g. pure and simple competition, predator-prey interactions….) it is possible to derive analytical conditions for the existence of Hopf points in the model. I am also interested to investigate if such oscillatory behavior is chaotic or can lead to chaos. For this part, the analysis is carried out mainly through numerical bifurcation techniques.
My latest work (Chem. Eng. Sci. Vol. 80, pp. 188 (2012)) concerns the old problem of pure and simple competition under time invariant conditions with clean feed conditions (i.e. sterile feed). It is known that species involved in such competition (when they grow solely on substrate) cannot coexist except at discrete values of dilution rates and oscillations are obviously ruled out. Efforts on the literature were carried out to study the conditions for the existence of oscillatory behavior. One way is to allow the biomass to be in the feed and the introduction of substrate inhibition kinetics. The other way is the use of two or more interconnected chemostats. However, although these efforts showed the existence of oscillatory behavior, there was no reports of the existence of chaotic behavior. In my work, I re-examined the same problem but assuming that the specific growth rates do not depend only on substrate but are inhibited by the biomass. I selected the Contois model to describe such growth rates. In my work I showed the existence not only of periodic behavior but also of chaotic behavior.
2- Simulations and control of chemical processes: In this area of research, I also applied elements of bifurcation theory to analyze the nonlinear behavior of some chemical processes (polymerization reactors, fluidized beds…) as well as the control of chaos. In some parts of this work I used chaos theory to analyze the behavior of fluidized beds through the processing of pressure drop time series.