In the research involving control systems, especially chaotic systems with controls for various actions, circuit realizations are implemented using SPICE, LabView or FPGA etc. What circuit realization do you recommend?
This really depends on the level of realization you are looking for. If you are looking for a generalized systematic overview, MATLAB/Simulink offers a block-by-block analysis which is almost unbeatable. If you are looking at a circuit-level realization, then SPICE is a tried and true standard. Especially because there are a multitude of models, packages, and parts that are already available for download that you can use.
My personal recommendation is to use SPICE if you intend to go from simulation to the potential of experiment. The main reason for this is because my work involves physically building the chaotic circuit and the controller using analog circuits. Too frequently I see papers with proposed schematics that will never work in a real experiment. Analog components such as current feedback op-amps and analog multipliers should be simulated with the SPICE Macro-Model of each component. So far I have found that TINA-TI has an adequate numerical solver that can handle chaos AND all the Macro-Models.
There is a point at which the controller is too complicated to implement in analog circuitry. Too much noise and component inaccuracy will lead to poor performance. At that point one should consider using a digital controller implemented using Simulink w/ RealTime Workshop, a microcontroller or FPGA.
An FPGA will give you the best sample time, Simulink may give you the worst depending on what kind of Target you use but is easiest to implement.
I think starting with Simulink is better, because you can verify your design by simulate it and you can pass to the Hardware implementation directly from your blocks especially when you use tools like Xilinx system generator.