1 Introduction .................................................. 1
2 General Dynamics: Mathematical Structures ..................... 5
2.1 The Postulation and its Foundation in Electromagnetic
Field Theory ............................................. 5
2.2 Homogeneous and Heterogeneous Passive Memory Systems .... 11
2.3 The Titanium Dioxide Memristor .......................... 23
2.4 More Uniqueness: Coupling and Memristive Telegraph
Equations ............................................... 27
3 Integrable Structure: Abel Dynamics and CCOS Method .......... 35
3.1 Integrable Structure I: Bernoulli Dynamics .............. 36
3.2 Integrable Structure II: Abel Dynamics .................. 38
3.3 Comparison of the Two Dynamics .......................... 43
3.4 Characterization: The Characteristic Curve of State
(CCOS) Method ........................................... 47
4 Spintronic Memristive Systems ................................ 51
4.1 Spintronics and Memristors .............................. 52
4.2 Feedback Spin-Valve Memristive Structure: GMR and
Classical Hall Effect ................................... 58
4.3 The Dynamics of the Spin-Valve Memristive System ........ 62
4.4 Stability Analysis I: Lyapunov Stability and Poincare
Map ..................................................... 66
4.5 Stability Analysis II: Spin-Valve System ................ 71
4.6 Remarks: Analogy and Heterogeneous Structure ............ 75
4.7 Categorization: Abel Dynamics Readdressed ............... 76
5 Memristive Neuromorphic Systems .............................. 79
5.1 Neuronal Communication: Spike-Timing-Dependent-
Plasticity (STDP) ....................................... 81
5.2 Triplet Rule in STDP .................................... 86
5.3 Pair-Based Memristive STDP Model: Spike-Shape and
Thresholds .............................................. 88
5.4 Incompatibility with Triplet Rule ....................... 91
5.5 Memristive STDP Model Compatible with Triplet Rule ...... 94
5.6 Relation to Biological Quantities: Short-Term
Plasticity ............................................. 100
6 Applications ................................................ 103
6.1 Digital: Nonvolatile Memory, Stateful Logic and
More ................................................... 103
6.2 Analogue: Neuromorphic Circuits, Programmable Analog
Circuits and More ...................................... 109
7 Summary and Perspective ..................................... 117
References ..................................................... 121
List of Abbreviations .......................................... 127
List of Figures ................................................ 129
Main Contribution of the Author ................................ 135
Curriculum Vitae ............................................... 137
Acknowledgement ................................................ 139
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