Heterogeneous network (HetNet) is now considered to be a promising technique for enhancing the coverage and reducing the transmit power consumption of the next 5G system. Deploying small cells such as femtocells in the current macrocell networks achieves great spatial reuse at the cost of severe cross-tier interference from concurrent transmission. In this situation, two novel energy efficient power control and resource allocation schemes in terms of energy efficiency (EE)-fairness and EE-maximum, respectively, are investigated in this paper. In the EE-fairness scheme, we aim to maximize the minimum EE of the femtocell base stations (FBSs). Generalized Dinkelbach's algorithm (GDA) is utilized to tackle this optimization problem and a distributed algorithm is proposed to solve the subproblem in GDA with limited intercell coordination, in which only a few scalars are shared among FBSs. In the EE-maximum scheme, we aim to maximize the global EE of all femtocells which is defined as the aggregate capacity over the aggregate power consumption in the femtocell networks. Leveraged by means of the lower-bound of logarithmic function, a centralized algorithm with limited computational complexity is proposed to solve the global EE maximization problem. Simulation results show that the proposed algorithms outperform previous schemes in terms of the minimum EE, fairness and global EE.

The main objective of this work is to provide a deep understanding of the periodic behaviour corresponding to a homoclinic related to the Takens-Bogdanov (double-zero eigenvalue of the linearization matrix) and the periodic behaviour of the torus bifurcation related to the Hopf-Pitchfork bifurcation (a pair of imaginary eigenvalues and the third one zero) corresponding to some sections of a triple-zero eigenvalue bifurcation in the Chua's equation with a cubic nonlinearity.