Stocks, Flows and Tipping Points: A System-Dynamics Toy of Anxiety-Addiction Feedback

1. A model in which every crisis ends well

The 2024 post ended on hope. It said that even entrenched cycles of anxiety and addiction can shift, and that breaking points, “while painful, often create the conditions necessary for lasting change”. The simulation seemed to show it: anxiety climbed, crossed a red dashed line, the status switched to “Recovery Phase”, a green band appeared on the chart and the curves came down.

They came down because line 108 of the code told them to. We wrote a model in which every crisis resolves, ran it, and reported that crises resolve. This paper takes that apart, keeps the structure that was worth having, and replaces the scripted ending with a question that can come out either way: does this kind of system give warning before it tips?

2. The original model

The code is a single Python file of 676 lines with a Tkinter interface. Five numbers between 0 and 100 change each step: anxiety (start 20), addiction (30), dopamine (50), serotonin (50) and tolerance (10). Twenty life events, ten negative and ten positive, move them by fixed amounts. A job loss, for example, adds 25 to anxiety and 15 to addiction and subtracts 10 from dopamine and 15 from serotonin. Events fire at random, more often and more negatively when anxiety is high. On top of that sit a handful of threshold rules, applied every third step: addiction above 50 raises anxiety, anxiety above 60 sometimes triggers “use” that raises addiction and briefly lowers anxiety, anxiety above 70 erodes serotonin, serotonin above 60 lowers anxiety. Every number in these rules was chosen by us. None comes from data or literature.

3. Audit

3.1 Recovery by design

Two separate code paths turn high anxiety into recovery:

# addiction_anxiety_simulation.py (commit 7f0efeb)
anxiety_threshold = 85  # breaking point threshold                      (line 64)

recovery_events = [                                                    # (lines 52-56)
    {"name": "Breaking point: Seeking help", "anxiety": -30, "addiction": -25, ...},
    {"name": "Breaking point: Lifestyle change", "anxiety": -35, "addiction": -30, ...},
    {"name": "Breaking point: Support system", "anxiety": -25, "addiction": -20, ...}
]

# Path 1, inside trigger_life_event(), lines 106-109
if anxiety_level > anxiety_threshold and not in_recovery_phase:
    # Trigger a recovery event at breaking point
    event = random.choice(recovery_events)
    enter_recovery_phase()

# Path 2, inside update_simulation(), lines 258-261, checked every third step
if anxiety_level >= anxiety_threshold and not in_recovery_phase and random.random() < 0.2:
    # Trigger a recovery event
    trigger_life_event(forced_event=random.choice(recovery_events))

Path 1 fires whenever a random life event comes due while anxiety is above 85, and it also starts a 60-step recovery phase in which negative events become rarer. Path 2 gives a 20% chance every third step. Either way, staying above the threshold for long is close to impossible.

To see how much of the model's behaviour this explains, we ran the published code headless, without the interface, for 50 seeds of 3,000 steps each. We then ran it again with the threshold set to 101, which anxiety can never reach because it is capped at 100. That switches both paths off and leaves everything else unchanged.

The remaining 30% of crossings fell back below 85 through random fluctuation or a positive event before the scripted event arrived. Without the rule, nothing in the model pulls anxiety back down for long: it spends almost half its time above the line and averages 80. The reinforcing rules dominate. The hopeful ending was a constant we typed in.

3.2 Two decorative variables

Dopamine rises with “use” and falls with tolerance. Tolerance rises when addiction is high. Neither is ever read by any rule that changes anxiety, addiction or serotonin. Delete both and the rules governing the other three variables stay exactly as they are. They were drawn on the chart and written up as neurochemistry, but they had no causal role in the simulation.

3.3 The neurochemistry labels

The post called dopamine “pleasure”. That reading has been out of date for three decades. Robinson and Berridge's incentive-sensitisation theory holds that mesolimbic dopamine mediates incentive salience, the “wanting” of a reward, rather than its hedonic impact, the “liking”, and that in addiction the wanting can grow while the liking does not [1]. Koob and Volkow describe addiction as a recurring cycle of three stages, binge and intoxication, withdrawal and negative affect, and preoccupation and anticipation, involving reward, stress and executive-control circuits [2]. A single gauge labelled pleasure is the wrong abstraction, and in this code it did nothing anyway.

The post called serotonin “wellbeing”. An umbrella review by Moncrieff and colleagues found no consistent evidence for an association between serotonin and depression [3]. That review has its critics, and the debate is not settled. Under any reading of it, one serotonin number standing for wellbeing is not defensible.

3.4 Rock bottom

The model encodes the idea that people recover after hitting bottom. The idea is common in recovery culture, but it has rarely been measured. Kirouac and Witkiewitz note that “hitting bottom” had not been formally operationalised before their own work, in which they developed a questionnaire to capture it [4]. A concept that research is still learning how to define should not be a law of a model. If it belongs in a simulation at all, it belongs there as a hypothesis with a switch.

3.5 Smaller points

• The post said that being in recovery “reduces the probability of negative events by 40%”. The code subtracts 0.4 from a probability that lies between 0.3 and 0.8, with a floor of 0.1. That is 40 percentage points, which for a starting probability of 0.5 is a reduction of 80%.
• The post linked to a GitHub address that does not exist. The code is at the address given in section 7.
• The post invoked strange loops, the ouroboros, samsara and Heidegger. We have dropped them. They did not do any work the feedback loops could not do more precisely.

4. Restated as stocks and flows

System dynamics describes a system by its stocks, the quantities that accumulate, the flows that fill and drain them, and the feedback loops that connect the two [5]. Restating the toy this way makes its assumptions visible and shows where the original was open-ended.

Four loops connect these stocks:

• R1, the relief trap. Anxiety drives use, which relieves anxiety in the short run. Use also builds dependence, and dependence feeds anxiety back through withdrawal. Balancing in the short run, reinforcing in the long run. The 2024 rules “anxiety above 60 triggers use” and “addiction above 50 raises anxiety” are this loop.
• R2, erosion. High anxiety wears down coping capacity, and lower capacity lets anxiety rise. The 2024 serotonin rules are this loop.
• R3, tolerance. Use builds tolerance, tolerance reduces relief per use, and lower relief drives more use. The 2024 code had the first link and dropped the rest.
• B1, coping. Coping capacity drains anxiety and, more slowly, dependence. Help-seeking belongs here: its likelihood should rise with anxiety and with remaining capacity, because asking for help takes some capacity. Nothing guarantees it fires.

The forced breaking point is gone. Recovery, if it happens, has to come from B1 winning against R1 and R2.

5. Proposed design: no forced recovery, and a test for early warning

5.1 The model

Four stocks updated in small time steps, with the loops above as flows, additive noise on anxiety, and exogenous stress as a slowly changing input. Life events stay, but as shocks of random size rather than a fixed menu. No parameter value is presented as calibrated. Every parameter is sampled from a stated range and the results are reported across the range.

# Proposed structure, not yet run. Parameter values are sampled, not fitted.
use      = sensitivity(A, T) * A                    # anxiety-driven use, damped by tolerance
relief   = relief_per_use / (1 + T) * use
dA = stress(t) + withdrawal * H - coping * C * A - relief + noise()
dH = use - extinction * H - treatment(A, C) * H
dT = build * use - decay * T
dC = support(t) - erosion * max(0, A - A_tolerable) * C

5.2 Questions, in order

1. Are there tipping points at all? Sweep stress slowly up and then down and look for hysteresis, a range where the system can sit either in a low-anxiety or in a high-anxiety, high-dependence state. If there is none for any plausible parameter range, there is nothing to warn about, and we will report that.
2. Do warnings appear before the shift? Near a fold, a system recovers more slowly from small disturbances. This critical slowing down shows up as rising variance and rising lag-1 autocorrelation in the fluctuations [6]. Van de Leemput and colleagues found that higher autocorrelation and variance in self-recorded emotions were associated with an upcoming shift into depression and out of it [7]. We test both directions.
3. How often do they lie? Indicators of this kind have error rates that are seldom reported. We follow Boettiger and Hastings and estimate false alarms and missed warnings directly [8].
4. Drift or shock? A large life event can push the system across without any slowing down beforehand. We expect warnings for transitions caused by slow drift in stress and none for transitions caused by single shocks, and we test that separately.

5.3 Method

At least 200 runs per condition with published seeds. A transition is a move into the high-anxiety basin that lasts for a fixed minimum time. For each transition we take the series before it, remove the trend with a Gaussian kernel, and compute variance and lag-1 autocorrelation in a rolling window of half the series length. The trend of each indicator is summarised by Kendall's tau, following the toolbox of Dakos and colleagues [9]. The same statistics are computed on matched runs at constant stress that do not tip. Performance is reported as a ROC curve and its area. Window sizes, bandwidths and the transition rule are fixed before the first run.

What would count as a result. An area under the ROC curve clearly above 0.5, with a confidence interval, for drift-driven transitions, and close to 0.5 for shock-driven ones, would support the use of these indicators in this class of model. Anything else is also a result, and we will publish it.

7. Reproducibility

Code. github.com/kim266/addiction_anxiety_simulation, commit 7f0efeb (9 April 2025), which matches our archived copy. The 2024 post linked to addiction_anxiety_simulation_simulation, which returns a 404.

Audit. We copied the file to a separate folder and imported it as a module; the interface only starts when the file is run directly. For each seed (0 to 49) we reloaded the module to reset its global state, called random.seed(seed) and called update_simulation() 3,000 times, recording anxiety after each step and the name of every triggered event. “Rule off” sets anxiety_threshold = 101 before the first step. A crossing is a step on which anxiety moves from below 85 to 85 or above. It counts as ended by the rule if a “Breaking point” event fires before anxiety falls below 85 again. The second-half statistics use steps 1,500 to 3,000. The audit runs in about one second.

Not run. Nothing in sections 4 and 5 has been run. The restated model and the early-warning analysis will be published with code and seeds when they are.