Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 24, Issue 5, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127414300158
Keywords
Hamiltonian; memristor; memristive device; dissipative circuit; conservation of momentum; conservation of charge and flux; conservation of energy; zero-crossing property; Newton's equation; Hamilton's equations; Chua's circuit; CNN
Funding
- AFOSR [FA 9550-13-1-0136]
- EC Marie Curie Fellowship
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In this paper, we show that Hamilton's equations can be recast into the equations of dissipative memristor circuits. In these memristor circuits, the Hamiltonians can be obtained from the principles of conservation of charge and flux, or the principles of conservation of energy. Furthermore, the dynamics of memristor circuits can be recast into the dynamics of ideal memristor circuits. We also show that nonlinear capacitors are transformed into nonideal memristors if an exponential coordinate transformation is applied. Furthermore, we show that the zero-crossing phenomenon does not occur in some memristor circuits because the trajectories do not intersect the i - 0 axis. We next show that nonlinear circuits can be realized with fewer elements if we use memristors. For example, Van der Pol oscillator can be realized by only two elements: an inductor and a memristor. Chua's circuit can be realized by only three elements: an inductor, a capacitor, and a voltage-controlled memristor. Finally, we show an example of two-cell memristor CNNs. In this system, the neuron's activity depends partly on the supplied currents of the memristors.
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