Time delay in the kinetic terms of reaction-diffusion systems has been investigated. It has been shown that short delay beyond a critical threshold may induce spatiotemporal instabilities. For unequal diffusivities and appropriate parameter space delay may induce Turing instability resulting in stationary patterns and also interesting Turing-Hopf transition with the formation of spirals. The theoretical scheme has been numerically explored in two different prototypical reaction-diffusion systems.

Time-delayed feedback is a practical method for controlling various nonlinear dynamical systems. We consider its influence on the dynamics of a multicycle van der Pol oscillator that is birhythmic in nature. It has been shown that depending on the strength of delay the bifurcation space can be divided into two subspaces for which the dynamical response of the system is generically distinct. We observe an interesting collapse and revival of birhythmicity with the variation of the delay time. Depending on the parameter space the system also exhibits a transition between birhythmicity and monorhythmic behavior. Our analysis of amplitude equation corroborates with the results obtained by numerical simulation of the dynamics.

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The selective control of O-H/O-D bond dissociation in reduced dimensionality model of HOD molecule has been explored through IR+UV femtosecond pulses. The IR pulse has been optimized using simulated annealing stochastic approach to maximize population of a desired low quanta vibrational state. Since those vibrational wavefunctions of the ground electronic states are preferentially localized either along the O-H or O-D mode, the femtosecond UV pulse is used only to transfer vibrationally excited molecule to the repulsive upper surface to cleave specific bond, O-H or O-D. While transferring from the ground electronic state to the repulsive one, the optimization of the UV pulse is not necessarily required except specific case. The results so obtained are analyzed with respect to time integrated flux along with contours of time evolution of probability density on excited potential energy surface. After preferential excitation from [line]0, 0> ([line]m, n> stands for the state having m and n quanta of excitations in O-H and O-D mode, respectively) vibrational level of the ground electronic state to its specific low quanta vibrational state ([line]1, 0> or [line]0, 1> or [line]2, 0> or [line]0, 2>) by using optimized IR pulse, the dissociation of O-D or O-H bond through the excited potential energy surface by UV laser pulse appears quite high namely, 88% (O-H ; [line]1, 0>) or 58% (O-D ; [line]0, 1>) or 85% (O-H ; [line]2, 0>) or 59% (O-D ; [line]0, 2>). Such selectivity of the bond breaking by UV pulse (if required, optimized) together with optimized IR one is encouraging compared to the normal pulses.

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An all-chemical analog of clock-wave-front model for somitogenesis is proposed. The spatial periodicity can be obtained by arresting the homogeneous oscillations in a typical two-component reaction-diffusion system in the Hopf region by interacting with a chemical wave front. The patterns can be controlled by tuning the wave speed of the front.

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