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The dynamical behaviour of the erbium-doped fibre single-ring laser with an optical delay feedback is discussed. Simulation shows that as the delay rate increases, the lasing light displays period-doubling which leads to chaos and via reverse period-doubling route returns from chaos to periodic. At a particular delay rate the intermittently chaotic route to chaos is also observed. The identical synchronization based on chaos in this ring laser is demonstrated by numerical simulation.

A two-dimensional time-delay chaotic system is designed and realized in an electronic circuit based on its dynamical behavior. Then a generalized synchronization chaotic system is designed by linear transformation method. The generalized synchronization condition is obtained by mathematical analysis, and generalized synchronization is realized in an electronic circuit. The results of numerical calculation conform the exactness and validity of theoretical analysis and circuit design.

A two-dimensional discrete system with chaotic and hyperchaotic characteristics has been designed and its dynamic behaviour has been analyzed, and the impulsiv e synchronization conditions have been obtained by mathematical analysis- In our experiment, impulsive synchronization of the circuit system has been realiz ed- The experimental data are in good agreement with the results of theoretical analysis and numerical calculation- In addition, the experimental results demons trate the effectiveness and robustness to noise by means of the above method

A two-dimensional discrete system with chaotic and hyperchaotic characteristics and the control of chaos and hyperchaos by means of time-delayed variable feedback have been realized in an electronic circuit.Both the complex behaviours in the circuit without control and the various stabilized periodic states in the controlled circuit are in good agreement with the results obtained by analyzing theoretically and simulating numerically.In addition,the experimental results confirm that it is effective to control chaos and hyperchaos by using the method of improved time-delayed variable feedback.