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Aiming at the problem that the global search performance of a transiently chaotic neural network is not ideal, a multiple frequency conversion sinusoidal chaotic neural network (MFCSCNN) model is proposed based on the biological mechanism of the brain, including multiple functional modules and sinusoidal signals of different frequencies. In this model, multiple FCS functions and Sigmoid functions with different phase angles were used to construct the excitation function of neurons in the form of weighted sum. In this paper, the inverted bifurcation diagram, Lyapunov exponential diagram and parameter range of the model are given. The dynamic characteristics of the model are analyzed and applied to function optimization and combinatorial optimization problems. Experimental results show that the multiple frequency conversion sinusoidal chaotic neural network has better global search performance than the transient chaotic neural network and other related models. [ABSTRACT FROM AUTHOR]

We use the residue harmonic balance scheme to study the periodic motions of a class of second-order delay-differential equations with cubic nonlinearities near and after Hopf bifurcation. The multiple solutions are found by homotopy continuation. Then, the approximation to any desired accuracy for a specific solution is captured by solving linear equations iteratively. The second-order solutions give good predictions for the frequency and amplitude, which are verified by the Runge–Kutta numerical solutions. Two typical examples, the temporal dynamics of the delay Liénard oscillator and the delay feedback Duffing system, are studied and compared. The results show how to trace analytically the relevant effect of the stiffness coefficient and the time delay on the dynamics and on the number of periodic solutions, even for large values of the bifurcation parameters. [ABSTRACT FROM PUBLISHER]