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Communications in Nonlinear Science and Numerical Simulation > 2017 > 53 > Complete > 111-129

_{1}and X

_{2}) and one predator (X

_{3}). Under some assumptions we prove that there are three numbers γ

_{1}> γ

_{2}> γ

_{3}which have the following properties: if γ

_{1}< 1, then all the populations go to extinction almost surely (a.s.), i.e., limt→+∞Xi(t)=0 a.s., i=1,2,3; If γi>1>γi+1,i=1,2,...

Communications in Nonlinear Science and Numerical Simulation > 2017 > 53 > Complete > 142-153

Communications in Nonlinear Science and Numerical Simulation > 2017 > 53 > Complete > 278-287

Communications in Nonlinear Science and Numerical Simulation > 2017 > 53 > Complete > 228-248

Communications in Nonlinear Science and Numerical Simulation > 2017 > 53 > Complete > 263-277

Communications in Nonlinear Science and Numerical Simulation > 2017 > 53 > Complete > 202-212

Communications in Nonlinear Science and Numerical Simulation > 2017 > 53 > Complete > 154-183

Communications in Nonlinear Science and Numerical Simulation > 2017 > 53 > Complete > 184-201

Communications in Nonlinear Science and Numerical Simulation > 2017 > 53 > Complete > 249-262

Communications in Nonlinear Science and Numerical Simulation > 2017 > 53 > Complete > 288-298

_{n,r}) is introduced as a new way to assess the complexity of a complex dynamical system such as stock market. We test the performance of this method with simulated data. Results show that N

_{n,r}with appropriate parameters is more sensitive to the change of system and describes the trends of complex systems clearly. In addition,...

Communications in Nonlinear Science and Numerical Simulation > 2017 > 53 > Complete > 130-141