Adaptive synapse-based neuron model with heterogeneous multistability and riddled basins.

Biological neurons can exhibit complex coexisting multiple firing patterns dependent on initial conditions. To this end, this paper presents a novel adaptive synapse-based neuron (ASN) model with sine activation function. The ASN model has time-varying equilibria with the variation of externally applied current and its equilibrium stability involves transitions between stable and unstable points through fold and Hopf bifurcations, resulting in complex distributions of attractive regions with heterogeneous multi-stability. Globally coexisting heterogeneous behaviors are studied by bifurcation diagram, phase portrait, dynamical distribution, and basin of attraction. The results show that the number of coexisting heterogeneous attractors can be up to 12, but for a simple neuron model, such a large number of coexisting heterogeneous attractors has not been reported in the relevant literature. Most interestingly, the ASN model also has riddled-like complex basins of attraction and four illustrative examples are depicted by the phase portraits with small changes of the initial conditions. Besides, the ASN model is implemented using a simple microcontroller platform, and various heterogeneous coexisting attractors are acquired experimentally to validate the numerical results.

Initial-switched boosting bifurcations in 2D hyperchaotic map.

Recently, the coexistence of initial-boosting attractors in continuous-time systems has been attracting more attention. How do you implement the coexistence of initial-boosting attractors in a discrete-time map? To address this issue, this paper proposes a novel two-dimensional (2D) hyperchaotic map with a simple algebraic structure. The 2D hyperchaotic map has two special cases of line and no fixed points. The parameter-dependent and initial-boosting bifurcations for these two cases of line and no fixed points are investigated by employing several numerical methods. The simulated results indicate that complex dynamical behaviors including hyperchaos, chaos, and period are closely related to the control parameter and initial conditions. Particularly, the boosting bifurcations of the 2D hyperchaotic map are switched by one of its initial conditions. The distinct property allows the dynamic amplitudes of hyperchaotic/chaotic sequences to be controlled by switching the initial condition, which is especially suitable for chaos-based engineering applications. Besides, a microcontroller-based hardware platform is developed to confirm the generation of initial-switched boosting hyperchaos/chaos.

Multistability in Chua's circuit with two stable node-foci.

Only using one-stage op-amp based negative impedance converter realization, a simplified Chua's diode with positive outer segment slope is introduced, based on which an improved Chua's circuit realization with more simpler circuit structure is designed. The improved Chua's circuit has identical mathematical model but completely different nonlinearity to the classical Chua's circuit, from which multiple attractors including coexisting point attractors, limit cycle, double-scroll chaotic attractor, or coexisting chaotic spiral attractors are numerically simulated and experimentally captured. Furthermore, with dimensionless Chua's equations, the dynamical properties of the Chua's system are studied including equilibrium and stability, phase portrait, bifurcation diagram, Lyapunov exponent spectrum, and attraction basin. The results indicate that the system has two symmetric stable nonzero node-foci in global adjusting parameter regions and exhibits the unusual and striking dynamical behavior of multiple attractors with multistability.

Long-range magnetic coupling across a polar insulating layer.

Magnetic interactions in solids are normally mediated by short-range exchange or weak dipole fields. Here we report a magnetic interaction that can propagate over long distances (∼10 nm) across a polar insulating oxide spacer. Evidence includes oscillations of magnetization, coercivity and field-cooled loop shift with the thickness of LaAlO3 in La0.67Sr0.33MnO3/LaAlO3/SrTiO3 heterostructures. Similar modifications of the hysteresis loop appear when two coupled films of La0.67Sr0.33MnO3 are separated by LaAlO3, or another polar insulator, but they are absent when the oxide spacer layer is nonpolar. The loop shift is attributed to strong spin-orbit coupling and Dzyaloshinskii-Moriya interaction at the interfaces. There is evidence from inelastic light scattering that the polar spacer mediates long-range transmission of orbital magnetization. This coupling mechanism is expected to apply for any conducting ferromagnetic oxide with mixed valence; in view of electron hopping frequency involved, it raises the prospect of terahertz tunability of magnetic coupling.