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In the paper, by using topological degree theory and Lyapunov function method, the issue of global robust stability is investigated for a class of interval bidirectional associative memory neural networks with inverse Lipschitz neuron activations, a novel sufficient conditions are established towards the existence, uniqueness and global robust stability of the equilibrium point, finally, a examples...
Complex chaotic dynamics is studies in the van der Pol oscillator model of business cycle forced by a sinusoidal function. The famous topological horseshoe theorem is applied to prove the existence of chaos from the mathematical viewpoint in this business cycle model. A rigorous proof for the existence of topological horseshoe is given. This technique combines the topological theory with the computer-assisted...
The paper analyzes a new hyper-chaotic Lu attractor which has rich and complex dynamical behaviors, by utilizing Lyapunov exponent spectrum, bifurcation diagram and phase portraits. And the local bifurcation is investigated by the centre manifold theorem. With the variation of parameters, the system will undergo pitchfork bifurcation and Hopf bifurcation at zero equilibrium, respectively. Finally,...
The current famous topological horseshoe theory is applied to an SEIR epidemic model with sinusoidally varying contact rate. For the first time, a rigorous computer-assisted verification of the existence of horseshoe chaos in this SEIR model is presented, which implies that chaos does exist from a theoretical and mathematical viewpoint other than the purely numerical computations viewpoint. By virtue...
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