{"id":"b50dce22-b8dc-4f41-b0a5-a7b550a35aa0","arxiv_id":"1908.01295","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"Time delays placed on selected nodes' links convert a fully synchronized network into a state where a few solitary nodes are displaced from the synchronized cluster, with the displacement and locations controlled by delay values and positions.","lead":"This paper shows that adding time delays to the connections of a few chosen nodes in a synchronized network makes those nodes drift away from the synchronized cluster, creating solitary states. It demonstrates the effect in two different model systems, offering a possible general way to engineer partial synchronization patterns.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central 'complete control' claim is not quantitatively established: the paper never verifies that solitary-node positions coincide with delayed-node positions for arbitrary selections, nor that displacement magnitude is a controlled function of delay value.","rationale":"The reader's weakest assumption is essentially the same: exact coincidence of delayed and solitary nodes. I agree with that identification. The central claim has two logically distinct parts, position and displacement; both are asserted without quantitative validation. The strongest independent support is the qualitative consistency across two very different dynamical systems (FHN oscillators and logistic maps), which suggests the phenomenon is real, but it does not establish the precision claimed. The correct response is to keep the manuscript CONDITIONAL: the phenomenon is plausible and clearly illustrated, but the control claim is not yet verified. I therefore recommend no change to the reader's verdict.","tokens_in":11550,"tokens_out":3530,"duration_ms":39582,"concrete_test":"Perform a systematic numerical experiment for both models: fix N=300, use 50 random realizations for each delayed-node count (e.g., 1, 5, 10, 25, 75, 125), plus structured patterns (contiguous block, alternating nodes, random). Define a solitary node quantitatively, e.g., time-averaged activator or mean phase velocity deviating by more than one standard deviation from the synchronized-cluster median. Compute precision and recall of the delayed-node set against the solitary-node set, and report the distribution of displacement versus delay value. If the sets are not identical for all tested patterns, or if displacement is not monotone and reproducible in delay value, the 'complete control' claim must be reduced to a tendency for sparse random delays.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's claim of complete spatial and quantitative control (Abstract; Section 6) requires two exact correspondences: (i) every delayed node appears as a solitary node, and every non-delayed node remains in the synchronized cluster; (ii) the solitary displacement is a known function of the assigned delay value. The manuscript supports these only with a handful of hand-picked visualizations (Figs. 2, 5, 7-10), and no quantitative measure of 'solitary' is defined. In particular, because Eq. (1) delays both incoming and outgoing links of a selected node, non-delayed neighbors receive delayed signals and could in principle also leave the cluster; conversely, a delayed node might remain effectively synchronized for small delay or strong coupling. The 125-delayed-node case (Fig. 4) already shows irregular spiking in a solitary node and a broadened limit cycle, suggesting that the correspondence may break down as the delayed fraction grows. Figures 9-10 show displacement varying with delay value, but only for a few values and without error bars, random realizations, or a stated relationship; the claim of complete control over displacement is therefore an extrapolation. No code, data, or statistical measures are provided, so the reader cannot check whether the displayed examples are representative.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes a technique for engineering solitary states in networks of identical oscillators by introducing time delays on all links of selected nodes. The authors study two systems: a ring of FitzHugh-Nagumo oscillators described by Eq. (1) and a ring of coupled logistic maps described by Eq. (3). They show, through phase portraits, time series, snapshots, mean-phase-velocity profiles, and spatial profiles, that placing homogeneous or heterogeneous delays on a subset of nodes can make those nodes leave the synchronized cluster while the rest remain synchronized. They further demonstrate a reverse scheme in which a fully delayed network is perturbed by altering delays on a few nodes. Based on these examples, the abstract and Section 6 claim that the position and displacement extent of solitary elements can be completely controlled by the positions and values of the incorporated delays.","tokens_in":11930,"tokens_out":3075,"duration_ms":33940,"significance":"If the central claim were quantitatively established, this would be a useful contribution to the control of partial synchronization patterns, particularly because the technique is demonstrated in two very different dynamical systems (FHN oscillators and chaotic maps), suggesting a potentially general mechanism. The paper also connects delay engineering of chimera states to the less studied solitary states. However, the current evidence is largely qualitative and illustrative: no quantitative definition of solitary state is given, no systematic parameter scans are provided, and no statistical verification over random realizations is reported. The claimed \"complete control\" therefore goes beyond what the presented data support.","major_comments":[{"comment":"The central positional-control claim requires demonstrating that, for arbitrary selections and parameter values, exactly the delayed nodes become solitary nodes and all non-delayed nodes remain in the synchronized cluster. The manuscript provides no quantitative definition of a solitary node, no measure of displacement from the cluster, and no statistics over random selections. Fig. 2 shows only 1, 5, and 25 delayed nodes, while Fig. 4 already shows a 125-delayed-node case where the solitary node exhibits irregular spiking and a smeared limit cycle, suggesting that the correspondence between delayed nodes and solitary nodes may break down as the delayed fraction grows. Please define a threshold-based measure (e.g., time-averaged deviation from the synchronized manifold or a phase-velocity difference), and report, over many random realizations and a range of delay values and delayed-node counts, the fraction of delayed nodes that are solitary and the fraction of non-delayed nodes that leave the cluster.","section":"Section 3, Figs. 2-4, Eq. (1)"},{"comment":"The claim that the extent of displacement is completely controlled by the delay value is not supported by the data. Figs. 9 and 10 show only a few selected delay values, with no quantitative measure of displacement on the vertical axis and no error bars or repeated realizations. No functional relationship between the delay time and the solitary-node displacement is derived, fitted, or systematically scanned. Please provide quantitative displacement-versus-delay curves for both homogeneous and heterogeneous delays, with multiple random realizations and statistical measures, and state whether the displacement is a single-valued and monotone function of the delay in the studied regime.","section":"Section 6 and Figs. 9-10"},{"comment":"Eq. (1) delays both the incoming and outgoing links of a selected node, so non-delayed neighbors also receive delayed signals and could in principle leave the synchronized cluster; conversely, a delayed node could remain effectively synchronized for small delay values or strong coupling. The manuscript does not analyze the parameter window in which exactly the delayed nodes become solitary nodes. The reverse scheme in Section 4 concludes that \"the mechanism works in both directions\" based only on qualitative snapshots in Fig. 6, without testing whether the number of solitary nodes equals the number of modified nodes. Please provide a regime analysis that identifies where the delayed-node-to-solitary-node correspondence holds, including boundary cases such as small delays and large numbers of delayed nodes.","section":"Sections 2 and 4"}],"minor_comments":[{"comment":"In the sentence \"we choose the delay times randomly in the interval τij. ∈ [1, 10]\" there is an extra period after τij; it should read τij ∈ [1, 10].","section":"Section 3"},{"comment":"In the model description for the maps, \"takes vale 1\" should be \"takes value 1\".","section":"Section 5"},{"comment":"The notation for the coupling range is inconsistent: Section 2 uses P/N with N=300 and r=0.35, while Section 5 uses K/N with r=0.32. Please unify the notation.","section":"Sections 2 and 5"},{"comment":"The paper does not report the numerical integration scheme, time step, or transient length used for the FHN simulations, nor the number of iterations and transient for the maps, which makes reproduction difficult. Please add these details.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The abstract and Section 6 substantially overstate the quantitative control that the presented evidence supports. I recommend requiring the additional quantitative analysis described in the major comments before publication, as the current manuscript is more a demonstration of principle than a verified control scheme."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is worth a serious referee, and I'd lean conditional-to-major-revision rather than reject. What's genuinely new is the transfer of the delay-node trick, previously used for chimera states, to solitary states: put delays on a chosen node's links and that node leaves the synchronized cluster. They show it works in two quite different systems (FHN oscillators and logistic maps), which is a real strength, and the reverse scheme (starting from all-delayed and perturbing a few nodes) adds robustness. The flat mean-phase-velocity profile for heterogeneous delays is a nice observation. The citation pattern is fine; the prior chimera-engineering work is their own but it's the obvious source.\n\nThe soft spots are mostly about the gap between what they show and what they claim. The abstract and conclusions say the position and displacement of solitary elements can be 'completely controlled.' What the figures actually demonstrate is a handful of examples where chosen delayed nodes do leave the cluster, with the number of solitary nodes roughly matching the number of delayed nodes and displacement varying with delay value. There is no systematic scan, no error bars across random realizations, no quantitative measure of 'solitary' (e.g., a displacement threshold), and no code. Fig. 4 already shows that at 125 delayed nodes the solitary node's dynamics become irregular and the limit cycle smears out, which suggests the clean correspondence may break down as the delayed fraction grows. The text notes this but doesn't quantify where the scheme stops working. The claim about controlling displacement is supported only by a few delay values; the relationship is not characterized. These are addressable rather than fatal issues. I'd want to see either a more careful statement of the claim ('can be influenced' or 'can be tuned for the studied regimes') or the additional simulations. There's no machine-checked proof or released code here, so I'm weighing the numerical evidence as presented.\n\nWho this is for: people working on partial synchronization, chimera/solitary states, and delay-coupled networks, especially those interested in control knobs for desynchronization patterns. It's a solid new application, not a paradigm shift. The reader's assessment (moderate confidence, conditional) matches mine; I'd be a bit less harsh on the novelty since transferring the scheme to a different pattern and showing flat frequency profiles is a real increment. The stress-test note is fair: the central claim is not quantitatively established, and I don't think that concern is misplaced.\n\nRecommendation: send to peer review. A serious referee can push for the missing statistics and a more precise statement, but the core phenomenon is clear and reproducible in principle. I would not desk-reject.","headline":"A useful engineering-style demonstration that placing delays on selected nodes' links induces solitary states in FHN rings and logistic maps, but the 'complete control' claim outruns the evidence.","tokens_in":12370,"tokens_out":662,"would_cite":true,"duration_ms":9191,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["05.45.-a","05.45.Xt"],"model":"deepseek-v4-flash","headline":"This paper claims that installing time delays on selected links in a synchronized network creates solitary states at exactly the delayed nodes, and that the delay values control how far each solitary node is displaced from the…","keywords":["solitary states","time delay","synchronization","FitzHugh-Nagumo","chaotic maps","partial synchronization","complex networks","delay engineering"],"falsifier":"Run the protocol for many random choices of delayed nodes and delay values in the FitzHugh-Nagumo network, and count how often the nodes that actually leave the synchronized cluster (identified by a deviation in mean phase velocity) coincide with the delayed nodes. A single realization in which a non-delayed node leaves the cluster, or a delayed node stays synchronized, would disprove the claim of complete control.","tokens_in":11338,"feed_emoji":"⏱️","tokens_out":7761,"duration_ms":68616,"temperature":0.7,"pith_summary":"This paper claims that a synchronized network of identical oscillators can be reshaped into a chosen partial synchronization pattern—solitary states—simply by putting time delays on all links of selected nodes. The position of each delayed node determines where a solitary node appears, and the delay value sets how far that node is displaced from the synchronized cluster. The claim is demonstrated in FitzHugh-Nagumo neural oscillators and in coupled chaotic logistic maps, with both homogeneous delays (equal displacement) and heterogeneous delays (unequal displacement). If true, this gives a practical control handle for desynchronizing a network at prescribed locations without changing coupling strengths or node parameters.","feed_headline":"Solitary states appear exactly where delays are placed","feed_subtitle":"In synchronized networks of oscillators and maps, choosing delay values sets how far each solitary node is displaced.","key_machinery":"The central object is the delayed node: a network node whose links to its neighbors all carry a time delay, either a common value (homogeneous) or randomly distributed values (heterogeneous). The delay acts as a perturbation that shifts the node's phase relative to the synchronized cluster, and the selective placement of these delayed nodes is what carves the solitary pattern out of a synchronized state. In FitzHugh-Nagumo networks the delay changes the limit cycle of the delayed node; in logistic maps it displaces the delayed node's state from the cluster. The paper uses the delay matrix to encode which links are delayed and by how much.","core_discovery":"The authors induce solitary states in networks that were originally fully synchronized. Delaying every ingoing and outgoing link of a chosen node perturbs that node out of the coherent cluster, producing the characteristic solitary state: a synchronized cluster coexists with individual nodes displaced in phase and mean velocity. With homogeneous delays, all solitary nodes are displaced by roughly the same amount; with heterogeneous delays, displacements differ. The same technique works in reverse, starting from an all-delayed synchronized network and changing the delay on a few nodes. The authors conclude that the number, position, and displacement of solitary states can be fully controlled by the positions and values of the delays.","pith_inferences":["A stronger, quantitatively testable version of the claim would be that the set of delayed nodes exactly equals the set of solitary nodes; the paper demonstrates this in examples but does not measure the match over many random delay placements, so a follow-up could check this one-to-one correspondence statistically.","If the one-to-one mapping holds, the method becomes a design primitive for network control: any prescribed solitary-state pattern can be written as a delay pattern, with implications for targeted desynchronization in power grids or neural stimulation protocols.","Since the delay value appears to set displacement, mapping displacement versus delay across a range (rather than the few values shown) would yield a calibration curve for how far a node can be pushed out of the cluster.","The reverse scheme suggests that delay patterns can be edited incrementally, so a network's solitary-state pattern can be trimmed or extended without resetting the whole system."],"forward_implications":["A desired number of solitary nodes can be placed at desired locations by installing delays on that many selected nodes at those locations.","Homogeneous delays give equally displaced solitary states; heterogeneous delays give unequally displaced ones, allowing tailored spatial patterns.","Starting from an all-delayed synchronized network, changing the delay on a few nodes (or removing it) creates solitary states in the same way, so the control works in both directions.","The same delay-engineering scheme produces solitary states in both continuous FitzHugh-Nagumo oscillators and discrete chaotic maps, suggesting a mechanism that does not depend on the specific node dynamics."],"supporting_citations":[{"why":"Defines solitary states in coupled oscillators and supplies the phenomenon this paper engineers via delays.","marker":"[Maistrenko et al.(2014)Maistrenko, Penkovsky, and Rosenblum]"},{"why":"Reports solitary states in FitzHugh-Nagumo networks, the neural model and phase-space structure used here.","marker":"[Mikhaylenko et al.(2019)Mikhaylenko, Ramlow, Jalan, and Zakharova]"},{"why":"Demonstrates delay-based engineering of chimera states, the method this paper adapts to solitary states.","marker":"[Ghosh and Jalan(2018)]"},{"why":"Introduces the rotational-coupling FitzHugh-Nagumo setup and parameter regime used as the base model.","marker":"[Omelchenko et al.(2013)Omelchenko, Omel’chenko, Hövel, and Schöll]"},{"why":"Shows solitary states in coupled chaotic maps, the second system used to test the technique.","marker":"[Rybalova et al.(2017)Rybalova, Semenova, Strelkova, and Anishchenko]"},{"why":"Documents solitary states in Kuramoto oscillators with inertia, establishing the broader context of the pattern.","marker":"[Jaros et al.(2015)Jaros, Maistrenko, and Kapitaniak]"}],"fun_headline_variants":["Delay placement and values steer solitary states","Controlling solitary states via delay design","Set solitary node offset by delay choice","Delayed links tune solitary states in networks"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that every node whose links are delayed becomes a solitary node and every non-delayed node remains in the synchronized cluster, so the delay pattern exactly marks the solitary-state pattern.","fun_headline_variants_meta":{"raw":{"variants":["Delay placement and values steer solitary states","Controlling solitary states via delay design","Set solitary node offset by delay choice","Delayed links tune solitary states in networks"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000158,"raw_usage":{"total_tokens":1132,"prompt_tokens":756,"completion_tokens":376,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":372,"completion_tokens_details":{"reasoning_tokens":324}},"tokens_in":372,"tokens_out":376,"duration_ms":5909,"temperature":1.0,"reasoning_tokens":324,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T15:16:36.148559+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the protocol for many random choices of delayed nodes and delay values in the FitzHugh-Nagumo network, and count how often the nodes that actually leave the synchronized cluster (identified by a deviation in mean phase velocity) coincide with the delayed nodes. A single realization in which a non-delayed node leaves the cluster, or a delayed node stays synchronized, would disprove the claim of complete control.","supporting_citations":[],"review_version":1}