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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...
Based on the well-known topological horseshoe theorem, a new rigorous computer-assisted proof for the existence of topological horseshoe in Chen's attractor is given. An appropriate Poincare section of Chen's attractor is chosen to obtain the corresponding Poincare map which is proved to be semi-conjugate to a 2-shift map. This implies that Chen's attractor has positive topological entropy, thus in...
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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